Ulster are now just two points ahead of Leicester after the Tigers' victory over Montpellier at Welford Road yesterday.
The result means Richard Cockerill's side keep up the pressure on the Pool Five leaders.
"We needed the five points and that was good for us," said Leicester director of rugby Cockerill.
"It keeps the pressure on Ulster but they're in the box seat. We've got to win next week at Montpellier really.
"We finish with Ulster here and we've still got Treviso which is no easy task either so there's a long way to go with some twists and turns. We'll see where we get to," he added.
Miles Benjamin capped his recovery from a serious neck injury with two tries in two minutes.
Benjamin's two tries for Leicester came after Vereniki Goneva's opener, with Jamie Gibson's score sealing the bonus point in the second half as Toby Flood kicked 18 points and Ryan Lamb added a late drop goal to deny Montpellier a bonus point.
Leicester had been leading 24-3, but Montpellier fought back with tries from Mamuka Gorgodze, former Ulster player Timoci Nagusa and two for Pierre Berard as they claimed a try bonus point of their own.
Jonathan Pelissie also kicked two penalties and two conversions, with captain Francois Trinh-duc also adding a conversion.
Cockerill was satisfied with the five points but bemoaned a lack of accuracy.
"We wanted to play today and we took our opportunities to score those first three tries very well, and then we had three or four more opportunities to score that we didn't take," Cockerill said.
"There were probably five or six tries left out there from both sides. We need to be more accurate.
"I don't think there will be as much life in the game next week than it was today but we'll see."