Tigers scored three tries in each half to secure the bonus-point victory against the Chiefs to move level on points with third-placed Bath.
Manu Tuilagi got the ball rolling with the opening score before Logovi’i Muilipola and top-scorer Vereniki Goneva added further tries before the break.
Tigers maintained the momentum after the break, grabbing the bonus-point score through Adam Thompstone before replacement David Mele added a brace late in the game.
Tuilagi made his first home appearance since the opening month of the season and partnered Anthony Allen at centre for the first time since last season’s Aviva Premiership Final.
Mathew Tait was a late withdrawal after he tweaked his ankle, with his place at full-back going to Scott Hamilton. Scrum-half Ben Youngs made the 100th starting appearance of his Tigers career, with Owen Williams at fly-half.
Exeter arrived at Welford Road on the back of their LV= Cup success last weekend, when they secured the Anglo-Welsh competition in front of their own Sandy Park fans.
And they made a good start, putting the first points on the board through Henry Slade’s seventh-minute penalty after Tigers were pinged at a ruck inside their own 22.
The Tigers reply was instant. Tuilagi’s bulldozing run down the left sucked in a couple of defenders and gave Leicester momentum. And the British & Irish Lion stayed out wide to receive Vereniki Goneva’s pass two phases later for a free run to the line. The touch judges ruled Williams’s conversion went wide despite protests from Tigers fans in the Holland & Barrett who felt the kick had gone over.
Goneva was the creator of the second try in the 13th minute. He broke Fetu’u Vainikolo’s tackle in midfield before a neat inside pass set Mulipola on a break through the tackle of last-man Jack Nowell and over behind the posts for his third try of the campaign. Williams added the conversion to give Tigers a 12-3 lead.
Williams struck a post with a penalty on 18 minutes but Ed Slater mopped up possession to maintain the pressure. Julian Salvi was stopped just short of the line before Allen kicked to the left corner where the ball beat Thompstone into touch. Play came back for a penalty advantage and Williams landed his kick to move Leicester 15-3 ahead.
A 5m lineout gave Exeter the chance to put pressure on Leicester defence for the first time. And they made the position and the possession count, hooker Jack Yeandle emerging from the back of the drive to score from close range. Slade landed the conversion to leave Tigers 15-10 ahead 12 minutes before half-time.
But again Tigers made a quick reply and again Goneva was instrumental. Crane broke the line and linked with Salvi before Goneva’s quick feet took him past Luke Arscott and Nowell to score. It was the 11th try of the season for Tigers’ leading scorer and when converted by Williams moved the hosts 22-10 ahead.
Exeter finished the half with 14 men after their captain Dean Mumm was shown a yellow card for a high tackle on Williams.
Goneva thought he had scored a second try six minutes from the break when he burst onto Ben Youngs’s pass but referee Dean Richards ruled it out for a forward pass. But Tigers had the advantage of a penalty and Williams stretched their lead at the break to 25-10.
Exeter's Matt Jess replaced Nowell at half-time.
Williams kept the scoreboard ticking over with a penalty early in the second half after an Exeter infringement at a ruck before Mumm returned to the action and Gareth Steenson replaced Vainikolo in the Chiefs backline.
Ben Moon’s bulldozing run took him past Goneva and Ben Youngs up to the Leicester 22 but he was unable to present clean ball forcing scrum-half Dave Lewis to hack ahead only to find his own man in an offside position.
Williams’s resulting penalty gave Tigers a lineout platform on the opposition 22. Tom Youngs and Crane secured clean ball, Allen set up the ruck and, at the next phase, Williams combined with Hamilton to send Thompstone over at the left corner for the bonus-point try. It gave Tigers a 33-10 lead.
Tigers made a raft of changes with David Mele, Toby Flood, Fraser Balmain, Thomas Waldrom, Graham Kitchener, Matt Smith and Rob Hawkins all introduced to the action.
Flood’s grubber had Arscott under pressure in the right corner, where his kick was charged into touch by Slater. Chiefs knocked on at the lineout to give Leicester the 5m scrum, which provided the platform for Mele to collect Waldrom’s pass for a simple score. Flood’s conversion gave Tigers a 40-10 lead.
Exeter scored a neatly-worked second try as the clocked ticked into the final 10 minutes. The visitors worked an overlap on the left where Tom Johnson fixed last man Matt Smith and gave Ian Whitten a free run to the line.
Tigers put together a smart move of their own with Flood, Kitchener and Goneva combining down the right before Gibson appeared to be tackled without the ball just short of the line. Referee Richards consulted his television match official seemingly for an act of foul play, but the TMO pulled play back for a forward pass at the start of the move.
But Tigers did have their sixth try with 90 seconds left. Mele’s quick penalty caught Exeter napping and he followed up Waldrom’s drive to score his second try and the final points of the game.