Steenson contributed 17 points with the boot
Haydn Thomas scored Exeter Chiefs' fourth and final try as they boosted their hopes of playing in the European Cup competition next season and ended rivals London Wasps' with a 37-24 bonus-point win.
The 30-year-old touched down in the 56th minute in the Premiership clash to add to Damian Welch's earlier score in the second half while Jack Yeandle and Jack Nowell grabbed tries in the first.
Wasps threatened to comeback first when Christian Wade danced through to make it 20-10 at half-time and then through Hugo Southwell's with the score 27-17 and James Scaysbrook in the bin.
However Thomas' try helped Exeter grab the bonus point while Gareth Steenson contributed 17 points with the boot in the form of four conversions and three penalties.
There was reason for Wasps to cheer with the last play of the game though as Tom Varndell broke to score his 13th try of the season setting a new club record in the process.
Exeter now occupy sixth, and the last European Cup spot for next season, in the table two points ahead of Bath Rugby while Wasps are eight adrift of them in eighth with one game left.
Exeter were penalised for not releasing the ball in the first minute of the game however Stephen Jones missed the resulting kick from a simple angle and distance.
Elliot Daly made no mistake four minutes later as the Chiefs were this time penalised for a double movement and Wasps went 3-0 ahead before the momentum swung to Exeter.
Steenson's fine break almost led to a try but Richie Baxter's bundle over was ruled out by the Television Match Official with no clear footage showing that the ball was grounded.
Steenson slotted the penalty that followed to level the scores before Welch broke from a Ben White pass in the 12th minute as Wasps turned over the ball.
Exeter worked their way to the left flank where Luke Arscott thrust to the line but fell short however Yeandle swept up to score the first try of the game.
Steenson converted and was then required to do the same minutes later as Thomas and Scaysbrook combined to feed Nowell for Exeter's second try.
A second Steenson penalty after 24 minutes made it 20-3 before Wasps responded with a fine try from flying winger Wade, which Jones converted.
Wade sliced through the Chiefs, breaking two tackles in the process to score, and threatened to repeat the trick moments later but passed forward.
Steenson then missed his first kick before the break as Exeter were awarded a penalty but they were back on the scoresheet within moments of the second half starting.
Welch exploited a hole to break and score with Steenson converting to make it 27-10 although Wasps responded with a try of their own through replacement Southwell.
That came moments after Scaysbrook was sent to the bin at Adams Park with Jones converting from the left flank to reduce the deficit to ten points.
Steenson missed an opportunity to pull Exeter ten clear with a penalty from distance before Thomas grabbed the bonus point try for the Chiefs with 24 minutes to play.
It was again converted by Steenson, making the score 34-17, before the fly-half added another three points with a penalty with 15 minutes left to play before Varndell's late converted consolation.
Tries: Wade, Southwell, Varndell
Cons: Stephen Jones 2, T Bell
For Exeter Chiefs:
Tries: Yeandle, Nowell, Welch, Thomas
Cons: Steenson 4
Pens: Steenson 3
Yellow card: James Scaysbrook (Exeter Chiefs, 48)
London Wasps: 15 Elliot Daly, 14 Christian Wade, 13 Andrea Masi, 12 Chris Bell (captain), 11 Tom Varndell, 10 Stephen Jones, 9 Joe Simpson, 8 Billy Vunipola, 7 James Haskell, 6 Ashley Johnson, 5 Joe Launchbury, 4 Tom Palmer, 3 Phil Swainston, 2 T Rhys Thomas, 1 Zak Taulafo.
Replacements: 16 Tom Lindsay, 17 Will Taylor, 18 Simon McIntyre, 19 Marco Wentzel, 20 Sam Jones, 21 Charlie Davies, 22 Tommy Bell, 23 Hugo Southwell.
Exeter Chiefs: 15 Luke Arscott, 14 Jack Nowell, 13 Phil Dollman, 12 Jason Shoemark, 11 Matt Jess, 10 Gareth Steenson, 9 Haydn Thomas, 8 Richard Baxter (captain), 7 James Scaysbrook, 6 Ben White, 5 Damian Welch, 4 Dean Mumm, 3 Hoani Tui, 2 Jack Yeandle, 1 Brett Sturgess.
Replacements: 16 Chris Whitehead, 17 Carl Rimmer, 18 Craig Mitchell, 19 Aly Muldowney, 20 Dave Ewers, 21 Will Chudley, 22 Henry Slade, 23 Ian Whitten.
Referee: Wayne Barnes
Assistant referees: Robin Goodliffe, Roy Maybank
TMO: David Grashoff