Edinburgh retain 1872 Cup
The win moved Edinburgh into fourth place while the Warriors are in eighth place on the Pro12 standings.
In Saturday's other match the boot of Ian Keatley proved the difference as Munster got back to winning ways with a narrow 9-7 victory over Ulster at Kingspan Stadium.
We look at Saturday's matches!
Glasgow Warriors 11-14 Edinburgh
The game was due to be played at Scotstoun, but because of the recent storm in Glasgow the teams met for the second time in succession at the national stadium, and just as they had a week ago, Edinburgh came out on top.
Unlike the first game though, it was a very tough encounter, with Glasgow leading going into the last ten minutes and going through an incredible 26 phases at the death only to be thwarted by the Edinburgh defence.
Mark Bennett's try on the half-hour had given Glasgow an 8-6 half-time lead, and after Duncan Weir and Sam Hidalgo-Clyne extended penalties, the Pro12 champions led 11-9 heading into the final stages.
But after a long period of pressure, Burleigh was allowed to run laterally before forcing his way over for the crucial score six minutes from time.
And while Glasgow had their chances at the death, they eventually saw a ball swallowed up in a maul and missed out on the win.
Glasgow started the better and led after just five minutes thanks to flyhalf Weir, as Edinburgh infringed while defending a line-out on their line.
However, a couple of breakdown penalties gave Sam Hidalgo-Clyne the chance to put his team in front and he made no mistake on either to leave the visitors, on home soil, 6-3 up.
Glasgow finally broke through with half an hour gone, Bennett the beneficiary after some patient build-up work from the Warriors pack.
That was how it remained until the break, with Weir missing the conversion, as well as kicking a penalty dead in goal after turning down three points.
He made up for it 15 minutes into the second half when he slotted a second penalty of the afternoon, with Hidalgo-Clyne having missed one five minutes earlier.
Hidalgo-Clyne was back on target with 11 minutes left to make it a two-score game, before Burleigh scored the crucial try.
And even though Glasgow had their chances, Edinburgh held on, to make it three wins on the spin against their closest rivals.
The scorers:
For Glasgow Warriors:
Try: Bennett
Pens: Weir 2
For Edinburgh:
Try: Burleigh
Pens: Hidalgo-Clyne 3
Teams:
Glasgow Warriors: 15 Stuart Hogg, 14 Taqele Naiyaravoro, 13 Mark Bennett, 12 Peter Horne, 11 Sean Lamont, 10 Duncan Weir, 9 Ali Price, 8 Josh Strauss, 7 Chris Fusaro, 6 Ryan Wilson, 5 Jonny Gray (captain), 4 Greg Peterson, 3 Zander Fagerson, 2 Fraser Brown, 1 Gordon Reid.
Replacements: 16 Shalva Mamukashvili, 17 Ryan Grant, 18 Sila Puafisi, 19 Leone Nakarawa, 20 Hugh Blake, 21 Grayson Hart, 22 Peter Murchie, 23 Lee Jones.
Edinburgh: 15 Jack Cuthbert, 14 Dougie Fife, 13 Michael Allen, 12 Matt Scott, 11 Damien Hoyland, 10 Phil Burleigh, 9 Sam Hidalgo-Clyne, 8 Cornell Du Preez, 7 John Hardie, 6 Mike Coman (captain), 5 Ben Toolis, 4 Anton Bresler, 3 WP Nel, 2 Ross Ford, 1 Rory Sutherland.
Replacements: 16 Neil Cochrane, 17 Allan Dell, 18 John Andress, 19 Alex Toolis, 20 Jamie Ritchie, 21 Sean Kennedy, 22 Greig Tonks, 23 Andries Strauss.
Referee: Peter Fitzgibbons (Ireland)
Assistant Referees: Lloyd Linton (Scotland), Graeme Wells (Scotland)
TMO: Jim Yuille (Scotland)
Ulster 7-9 Munster
The visitors came into the match on the back of three consecutive Pro12 defeats but two penalties and a drop goal for Keatley got them over the line at Ulster.
Keatley was in the thick of the action from the off as he turned over his first penalty inside ten minutes before a Louis Ludik try put Ulster in control.
It looked like the hosts would do enough to hold off the Munstermen but a drop goal and a late penalty saw Keatley put his side in front before they survived a late scare as Paddy Jackson missed from the tee with two-minutes left on the clock.
Munster started on the front foot and had their first chance for points in the eighth minute with a penalty that Keatley turned over.
Ulster burst to life after 11 minutes with a break down the left earning a line-out inside the 22. That worked the hosts in a strong position as they tried to force their way over the line but Anthony Foley's men held firm and a Munster penalty ensured the danger was cleared.
It was far-from a festival of free-flowing rugby but both sides were pushing for the game's first try with the hosts producing some strong set pieces in Munster territory and the visitors responding with a brilliant break on the right from Rory Scannell.
Ulster were looking the most likely and some sustained pressure on the Munster line after 23 minutes eventually paid dividends as Ludik forced his way over and Jackson converted.
With time ticking down in the first half Munster went on the offensive with a good Keatley kick moving the visitors up the five-metre line but Ulster held firm.
Munster went on the attack early in the second half but, despite moving the ball well from side to side, Ulster were resolute and once again repelled their advances.
With 15 minutes of the second half gone it was deadlock in the middle of the park with both sides probing but neither able to produce the moment of magic needed to pry open the opposition defence.
Munster were doing a good job of combating the Ulster attack and they finally had some more points on the board after 57 minutes as Keatley turned over a drop goal from just outside the 22 to make it a one-point game.
And they had the lead on the hour with the hosts penalised on their own 22 and Keatley remaining perfect from the tee to give his side a 9-7 advantage.
The hosts had the chance to reclaim the lead three minutes later with Munster penalised for collapsing the scrum but Jackson's kick fell just short.
Ulster refused to panic but, with five minutes left, they had created little in response to the Munster comeback.
But, with two minutes remaining, Jackson had the chance to give his side the win from the tee but his penalty sailed wide and Anthony Foley's men took the points back to Thomond Park.
The scorers:
For Ulster:
Try: Ludik
Con: Jackson
For Munster:
Pens: Keatley 2
DG: Keatley
Teams:
Ulster: 15 Louis Ludik, 14 Andrew Trimble, 13 Luke Marshall, 12 Stuart McCloskey, 11 Rory Scholes, 10 Paddy Jackson, 9 Ruan Pienaar, 8 Nick Williams, 7 Chris Henry, 5 Robbie Diack, 5 Franco van der Merwe, 4 Lewis Stevenson, 3 Wiehahn Herbst, 2 Rory Best (captain), 1 Kyle McCall.
Replacements: 16 Rob Herring, 17 Callum Black, 18 Ricky Lutton, 19 Alan O'Connor, 20 Roger Wilson, 21 Paul Marshall, 22 Ian Humphreys, Sammy Arnold.
Munster: 15 Andrew Conway, 14 Ronan O'Mahony, 13 Francis Saili, 12 Rory Scannell, 11 Lucas Gonzalez Amorosino, 10 Ian Keatley, 9 Tomás O'Leary, 8 CJ Stander (captain), 7 Tommy O'Donnell, 6 Jack O'Donoghue, 5 Mark Chisholm, 4 Dave Foley, 3 BJ Botha, 2 Mike Sherry, 1 Dave Kilcoyne.
Replacements: 16 Niall Scannell, 17 John Ryan, 18 Mario Sagario, 19 Billy Holland, 20 Robin Copeland, 21 Duncan Williams, 22 Tyler Bleyendaal, 23 Denis Hurley.
Referee: Gary Conway (Ireland)
Assistant referees: Sean Gallagher (Ireland), Brian MacNeice (Ireland)
TMO: Alan Rogan (Ireland)