Ulster bag crucial win in Edinburgh
Duncan Weir kicked in-form Edinburgh ahead in the first half but Ulster soon responded with scores for Darren Cave, Charles Piutau and John Cooney.
Weir responded with a breakaway try but the home side trailed at the break and never got back on even terms.
The Scottish side did get a second-half penalty try but Henderson's late effort was enough to bring Ulster within eight points of third-placed Edinburgh in the Conference B table.
The home side struck first in the match after Rory Best had been penalised at the breakdown, with Weir kicking a simple three-pointer.
But Ulster soon fired into gear and scored a superb try on 13 minutes, with fullback Piutau offloading out wide to Jacob Stockdale who passed back inside to Cave for the score.
Cooney added the extras and Weir kicked another penalty before Ulster went over for their second try, with Cave finding space on the overlap and passing on for Piutau to crash through any remaining defence.
Richard Cockerill's men should've heeded the warnings but didn't, with Ulster's third try showing similarities to their second, this time Stockdale on the outside break and passing inside to Cooney.
Weir decided to intervene in Ulster's enjoyable opening to the game though and at the next lineout gambled on an intercept – a gamble which paid off and left him with an unopposed run to the sticks.
Ulster led 19-13 at the break and soon extended that lead by three points on 51 minutes when Cooney struck once more.
Edinburgh's pack got the home side back in it though, with a spell of concerted pressure inside the Ulster 22 eventually resulting in a penalty try.
Cooney once again edged the visitors further ahead minutes later, with the lead at 25-20 with 15 minutes left to play.
Edinburgh have been in superb form of late, their only defeat in the last nine rounds coming at Glasgow on December 30, and there was plenty of effort and endeavour in the final 10 minutes.
Weir attempted a cross-field kick late on but it somehow found its way to Stockdale, who fed McCloskey, but the centre’s last-ditch offload fell to ground.
There was still time though for Ulster to get the crucial bonus-point score, as a series of drives towards the Edinburgh line eventually saw Henderson power over.
Tries: Weir, Penalty Try
Pens: Weir 2
Tries: Cave, Cooney, Piutau, Henderson
Cons: Cooney 3
Pens: Cooney 2
Edinburgh: 15 Blair Kinghorn, 14 Dougie Fife, 13 Mark Bennett, 12 Phil Burleigh, 11 Duhan van der Merwe, 10 Duncan Weir, 9 Sam Hidalgo-Clyne, 8 Bill Mata, 7 Jamie Ritchie, 6 Magnus Bradbury, 5 Grant Gilchrist, 4 Ben Toolis, 3 Simon Berghan, 2 Stuart McInally (captain), 1 Jordan Lay.
Replacements: 16 Neil Cochrane, 17 Rory Sutherland, 18 WP Nel, 19 Lewis Carmichael, 20 Cornell du Preez, 21 Sean Kennedy, 22 Jaco van der Walt, 23 Chris Dean.
Ulster: 15 Charles Piutau, 14 Louis Ludik, 13 Darren Cave, 12 Stuart McCloskey, 11 Jacob Stockdale, 10 Johnny McPhillips, 9 John Cooney, 8 Jean Deysel, 7 Nick Timoney, 6 Matthew Rea, 5 Iain Henderson, 4 Matthew Dalton, 3 Tom O'Toole, 2 Rory Best (captain), 1 Andy Warwick.
Replacements: 16 Rob Herring, 17 Tommy O'Hagan, 18 Rodney Ah You, 19 Alan O'Connor, 20 Sean Reidy, 21 David Shanahan, 22 Angus Curtis, 23 Tommy Bowe.
Referee: Nigel Owens (Wales)
Assistant referees: Wayne Davies (Wales), David Sutherland (Scotland)
TMO: Sean Brickell (Wales)