Simpson ran-in two tries in the third quarter to land damaging blows on Paul Gustard's men who launched two brave but futile fightbacks.
A 71st-minute penalty by Lima Sopoaga ultimately proved the difference but once hooker Elia Elia had crossed, Quins had one final chance to claim a top-four finish at Northampton's expense.
Replacement fly-half James Lang lined up a long-range penalty from just inside his own half but the kick fell narrowly short in a painful final act of the game.
Northampton's defeat at Exeter had given the London club sight of the play-offs but by losing in Coventry they allowed Saints to edge through.
Simpson, Elliot Daly, Nathan Hughes, Willie Le Roux and Jake Cooper-Woolley were playing their final games for Wasps, and while a route into the Champions Cup though a top-six finish proved elusive, they at least said farewell with a victory.
England head coach Eddie Jones and new Rugby Football Union chief executive Bill Sweeney watched from the stands as Wasps became the first to strike when a quickly-taken free-kick by Nathan Hughes was spun wide.
Poor positioning from Joe Marchant offered a sniff of the line and after he was easily rounded by Daly, Le Roux ran an arching line that drew in Mike Brown and fed the scoring pass to Josh Bassett.
But Quins, who had landed an earlier penalty, regained the lead when a counter-attack by Brown ended with Marchant breaking two tackles to touch down.
Jones watched on nervously as first-choice England tighthead Kyle Sinckler received treatment for a knock to his left ankle that required heavy strapping, and when play resumed Le Roux launched another raid that was ultimately foiled by Chris Robshaw.
Quins spent the rest of the half defending their own territory as Wasps used quick ball to launch waves of attacks orchestrated by Sopoaga but with little end reward.
Sopoaga landed a penalty, however, to give the home side a narrow interval lead and the one-way traffic continued after the break.
The pressure was building and Quins finally cracked in the 51st minute, with their defence stretched to breaking point following carries from Daly and Kieran Brookes that allowed Simpson to pick up and accelerate through a gaping hole to touch down.
Two departing players combined beautifully for Wasps' third try as Daly showed his pace in a trademark run before picking out Simpson with a perfect scoring pass.
Quins were stung into action and they responded when Danny Care scored a try that was impossible to prevent as he picked up from short range and placed the ball down by the post.
The one-way traffic was now fully reversed as Wasps became the side desperately trying to protect their win, in the process facing the unusual sight of Sinckler acting as playmaker.
Although Alex Dombrandt lost the ball just short of the line when a try looked certain, Quins succeeded shortly after when Elia Elia finished a forward drive over the line. And when Lang failed with his long range penalty, it was over.