Crossings from Alan O’Connor, Will Addison and Jacob Stockdale sealed an opening pool win, with John Cooney adding nine points off the tee.
Leicester headed into the interval leading by a slender three-point margin in a low-scoring half of rugby, which ended 3-0 in tough conditions.
George Ford fired over that penalty in the 15th minute after Tigers had weathered an early sustained period of pressure from the home side.
The England fly-half however would soon find himself heading to the sin-bin after making a high tackle on Ulster full-back Michael Lowry. Fortunately for Ford his absence did not yield any points against his side, as it remained 3-0 to Leicester when he returned on 32 minutes.
In fact the scoreline would not be altered before half-time, despite an Ulster surge on 35 minutes and then Ford’s charged down drop-goal.
Things improved and quickly in the second period for Ulster when lock O’Connor finished well from close range after a line-out move. That was converted by Cooney and one minute later they thought they had scored again, but Iain Henderson’s try was denied due to a forward pass.
Leicester, 7-3 down, went in search of a response and on 51 minutes they had a chance five metres out until a crooked line-out foiled them.
Ulster however made no such mistake as just before the hour mark centre Addison ran hard and straight and with Cooney’s extras it was 14-3.
Cooney made it 17-3 with 11 minutes left before a wonderful pass from McCloskey sent Stockdale over to leave Ulster needing one more try for the bonus point.
But it was Leicester who would have the final say, Manu Tuilagi sliding over in the wet for a morale-boosting score, with the game ending in entertaining fashion.
Tries: O’Connor, Addison, Stockdale
Cons: Cooney 3
Ulster: 15 Michael Lowry, 14 Craig Gilroy, 13 Will Addison, 12 Stuart McCloskey, 11 Jacob Stockdale, 10 Billy Burns, 9 John Cooney, 8 Nick Timoney, 7 Jordi Murphy, 6 Marcell Coetzee, 5 Iain Henderson, 4 Alan O’Connor, 3 Ross Kane, 2 Rory Best (c), 1 Andrew Warwick
Replacements: 16 Adam McBurney, 17 Eric O’Sullivan, 18 Marty Moore, 19 Kieran Treadwell, 20 Sean Reidy, 21 David Shanahan, 22 Angus Curtis, 23 Angus Kernohan
Leicester Tigers: 15 Jonah Holmes, 14 Adam Thompstone, 13 Manu Tuilagi, 12 Kyle Eastmond, 11 Jordan Olowofela, 10 George Ford, 9 Ben Youngs, 8 Sione Kalamafoni, 7 Brendon O’Connor, 6 Guy Thompson, 5 Harry Wells, 4 Mike Williams, 3 Dan Cole, 2 Tom Youngs, 1 Greg Bateman
Replacements: 16 Tatafu Polota-Nau, 17 David Fe’ao, 18 Joe Heyes, 19 Sam Lewis, 20 Tommy Reffell, 21 Sam Harrison, 22 Matt Toomua, 23 Gareth Owen
Referee: Pascal Gaüzère (France)
Assistant referees: Maxime Chalon (France), Jean-Luc Rebollal (France)
Television match official: Eric Gauzins (France)