Tigers maul Sarries
Manu Tuilagi and Greg Bateman both went over to give Tigers the lead with Veainu's powerful run ensuring the visitors led 21-6 at the break.
Jonah Holmes added the bonus point score on 64 minutes but there was still time for replacement Max Malins to get two late tries for Saracens.
The Tigers ended a run of seven straight away losses in all tournaments and secured their first league win over Saracens since March 2016.
London Irish won just their second game of the Premiership season with a battling victory over Worcester Warriors.
The only try of the game was scored by scrumhalf Piet van Zyl in the first half, but the Exiles had Greig Tonks to thank for kicking 17 points on their way to victory.
Chris Pennell responded from the tee for the visitors, but Worcester couldn't create any real try-scoring opportunities.
London Irish 22-9 Worcester Warriors
Worcester started well, pinning Irish back deep in their 22, and when Teofilo Paulo was penalised for a dangerous tackle and sin-binned, Chris Pennell stepped up to slot the penalty between the posts.
Irish hit back with two penalties of their own, but not before coming close to the game's first try.
Alex Lewington, making his 100th appearance for Irish found space on the left wing and chipped through for Piet van Zyl to run on to, but he was hauled down a yard from the line.
Van Zyl did manage to cross the line a few minutes later, finding a great line to break through the Warriors defensive line and gathering the ball from his own chip over the top to score.
It was a favourable bounce for the scrumhalf, but he pounced to put the home side into a deserved lead.
Arno Botha looked lively and cause the Warriors a few problems, but they gradually grew into the half and reduced the deficit with another Pennell penalty on 37 minutes.
Irish had lost from a better position against Northampton Saints in Round 15 and knew they would need a strong start after the interval.
When Worcester were penalised for not rolling away, Greig Tonks had an easy chance to extend the home side's advantage.
Worcester soon responded with a penalty of their own, Pennell calmly converting once again after Sam Lewis had burst forward into the Exiles' 22.
The game became quite cagey in the second half, with both sides conceding penalties when in attacking positions, unable to put points on the board, Tonks missing the chance to extend his side’s lead once more.
But the Warriors' indiscipline would cost them again, conceding another kickable penalty, with which Tonks made no mistake.
With the game all but won, wing Joe Cokanasiga broke from inside his own half and Irish came close to a second try, but settled for Tonks’ fifth penalty and a welcome victory.
For London Irish:
Try: Van Zyl
Pens: Tonks 5
Pens: Pennell 3
London Irish: 15 James Marshall, 14 Joe Cokanasiga, 13 Tom Fowlie, 12 Johnny Williams, 11 Alex Lewington, 10 Greig Tonks, 9 Piet van Zyl, 8 Ofisa Treviranus, 7 Conor Gilsenan, 6 Arno Botha, 5 Teofilo Paulo, 4 Franco van der Merwe (captain), 3 Ollie Hoskins, 2 David Paice, 1 Ben Franks.
Replacements: 16 Dave Porecki, 17 Harry Elrington, 18 Petrus Du Plessis, 19 Sebastian De Chaves, 20 Jake Schatz, 21 Scott Steele, 22 Tommy Bell, 23 Aseli Tikoirotuma.
Worcester Warriors: 15 Josh Adams, 14 Bryce Heem, 13 Chris Pennell, 12 Ryan Mills, 11 Dean Hammond, 10 Jamie Shillcock, 9 Francois Hougaard, 8 GJ van Velze, 7 Sam Lewis, 6 Alafoti Faosiliva, 5 Darren Barry, 4 Donncha O’Callaghan (captain), 3 Nick Schonert, 2 Jack Singleton, 1 Ethan Waller.
Replacements: 16 Kurt Haupt, 17 Ryan Bower, 18 Gareth Milasinovich, 19 Anton Bresler, 20 Will Spencer, 21 Matt Cox, 22 Jonny Arr, 23 Tom Howe.
Referee: JP Doyle
Assistant referees: Paul Dix, Anthony Woodthorpe
TMO: David Grashoff
Saracens 20-28 Leicester Tigers
Leicester opened the scoring on seven minutes as Manu Tuilagi burst through from behind ruck to to dot down his third try of the season.
Flyhalf Matt Toomua added the extras with Saracens replying through a Ben Spencer penalty.
Greg Bateman then spotted a gap at the ruck and sped away from the Saracens defence for the Tigers' second try on 33 minutes.
Spencer again reduced the deficit but Telusa Veainu then collected a Toomua offload before charging away from the Saracens defence to score.
Nathan Earle twice thought went close for Saracens after half-time only for the TMO to twice rule out the score as the winger dropped the ball.
And Tigers secured the bonus point when Tuilagi capitalised on a Saracens mistake to send Jonah Holmes away with Toomua knocking over his fourth conversion.
Max Malins danced through the Tigers defence for a consolation score on 69 minutes with Alex Lozowski adding the extras before Michele Rizzo was shown a yellow card.
And the Saracens replacement repeated the trick in the final minute but Saracens ran out of time to secure the losing bonus point.
Tries: Malins 2
Cons: Lozowski 2
Pens: Spencer 2
Tries: Tuilagi, Bateman, Veainu, Holmes
Cons: Toomua 4
Saracens: 15 Alex Goode, 14 Nathan Earle, 13 Marcelo Bosch, 12 Brad Barritt, 11 Chris Wyles, 10 Alex Lozowski, 9 Ben Spencer, 8 Jackson Wray, 7 Schalk Burger, 6 Calum Clark, 5 Nick Isiekwe, 4 Dominic Day, 3 Juan Figallo, 2 Schalk Brits, 1 Richard Barrington.
Replacements: 16 Scott Spurling, 17 Hayden Thompson-Stringer, 18 Titi Lamositele, 19 Mark Flanagan, 20 Sione Vailanu, 21 Tom Whiteley, 22 Max Malins, 23 Rotimi Segun.
Leicester Tigers: 15 Telusa Veainu, 14 Adam Thompstone, 13 Manu Tuilagi, 12 Gareth Owen, 11 Jonah Holmes, 10 Matt Toomua (captain), 9 Sam Harrison, 8 Sione Kalamafoni, 7 Brendon O’Connor, 6 Mike Williams, 5 Graham Kitchener, 4 Mike Fitzgerald, 3 Logovi’i Mulipola, 2 Tatafu Polota-Nau, 1 Greg Bateman.
Replacements: 16 Tom Youngs, 17 Michele Rizzo, 18 Pat Cilliers, 19 Harry Wells, 20 Luke Hamilton, 21 Harry Simmons, 22 Joe Ford, 23 Mathew Tait.
Referee: Craig Maxwell-Keys
Assistant referees: Adam Leal, Peter Allan
TMO: Sean Davey