Geoff Parling scored a try against his future club as Leicester battled past Exeter 25-18 at Welford Road.
Despite two tries from Thomas Wadrom and Will Chudley, Exeter paid the price for their indiscipline with Freddie Burns slotting six penalties for the Tigers.
With both sides desperately hunting down a place in the top four with the season on the final stretch, it was Tigers who started on the front foot thanks to a penalty from Burns, after finding themselves held up six metres out.
Immediately from the restart, the Chiefs reclaimed the ball, taking advantage of a gap in the Leicester defence and kicking towards the corner.
The resultant drive tested the Tigers, who were eventually able to hold it up on the line and in the process win the ball back, keeping their lead in tact.
Burns doubled the advantage with a second penalty as the clock approached 20 minutes, but a spectacular kick from his own half from Henry Slade halved the deficit, after missing two earlier chances in the opening seven minutes.
Exeter dominated for long spells of the half, and looked certain to get more points on the board when given a penalty advantage.
But despite going for the try rather than the three points, they couldn't break down the Leicester defence, eventually losing possession in the corner.
Burns added two more penalties, the second coming after the hosts came up just short of the try-line, as Tigers went into the break with a nine-point lead.
It took less than two minutes of the second half for Tigers to stretch that lead, Burns taking his points tally to 15 for the afternoon in an impressive showing from the kicker.
But Exeter grabbed the game's first try, Waldrom scoring it against his former side. It all came from Exeter winning a penalty in the Tigers 22, and Waldrom was the man at the bottom of a drive as the Chiefs got back in it.
The decision drew the anger of the Tigers squad, who didn't believe the ball had in fact crossed the line, but they were given something to smile about when Slade once again misfired, hitting the upright from what looked a straightforward position, squandering more points for his side.
Leicester refused to let that effort derail their performance, and almost got their first try but for a last ditch challenge on Vereniki Goneva, as Tigers threatened to go back clear.
They came even closer seconds later, Exeter refusing to let the ball be grounded however, as the Chiefs fought to salvage something from the game.
But Tigers pressure told, and Parling grabbed the first try for the hosts. Parling went over in the left corner after more possession, and Burns' conversion was solid, extending his faultless form in front of the posts.
The Chiefs went back into the try-scoring stakes however, when Slade's break forward saw him bear down on the line, before releasing to Will Chudley who went over. Slade converted, and with just over ten minutes to go, Exeter were within a converted try.
The irresistible right boot of Burns continued to keep the scoreboard ticking, as he continued his 100% record into a seventh kick, vitally taking the lead upto 10 points in the process.
Searching for that losing bonus point, Slade jinked his way through bodies before feeding Dave Lewis, who was crowded out before eventually knocking on.
But just as Tigers looked to kick the ball out to seal the win, they conceded a penalty, offering Slade the opportunity to secure his side a point. Despite a less than perfect afternoon for the fly-half, he delivered as Exeter managed to take away the bonus point.
Pens: Burns 6
Tries: Waldrom, Chudley
Pens: Slade 2
Leicester Tigers: 15 Mathew Tait, 14 Adam Thompstone, 13 Matt Smith, 12 Seremaia Bai, 11 Miles Benjamin, 10 Freddie Burns, 9 Ben Youngs (c), 8 Jordan Crane, 7 Julian Salvi, 6 Jamie Gibson, 5 Geoff Parling, 4 Sebastian de Chaves, 3 Dan Cole, 2 Tom Youngs, 1 Marcos Ayerza
Replacements: 16 Leonardo Ghiraldini, 17 Logovi'i Mulipola, 18 Fraser Balmain, 19 Jack Whetton, 20 Laurence Pearce, 21 Sam Harrison, 22 Tommy Bell, 23 Vereniki Goneva
Exeter Chiefs: 15 Phil Dollman, 14 Ian Whitten, 13 Jack Nowell, 12 Sam Hill, 11 Matt Jess, 10 Henry Slade, 9 Will Chudley, 8 Thomas Waldrom, 7 Dean Mumm (c), 6 Dave Ewers, 5 Damian Welch, 4 Mitch Lees, 3 Tomas Francis, 2 Jack Yeandle, 1 Carl Rimmer
Replacements: 16 Elvis Taione, 17 Ben Moon, 18 Alex Brown, 19 Ben White, 20 Kai Horstmann, 21 Dave Lewis, 22 Gareth Steenson, 23 Tom James
Venue: Welford Road, Leicester
Referee: JP Doyle
Assistant Referees: Gareth Copsey, Andy Watson
TMO: Rowan Kitt