Saracens scored a late try to snatch a 31-25 win over Sale, while there were also Premiership wins for Gloucester, Harlequins, Bath, Northampton and Exeter.
The defending champions looked set for a comfortable win after taking a 21-13 half-time lead at home, but Sale loanee Robert du Preez kept them in the game by scoring 20 points through a dead-eye kicking display.
After Du Preez’s first penalty gave the Sharks an early lead, Saracens scored 21 points, despite losing lock Will Skelton to a yellow card, thanks to tries from Michael Rhodes, Alex Lewington and Nick Tompkins.
However, Sale got themselves back into the contest just before the break when Faf de Klerk combined with Du Preez to release Byron McGuigan for their only try of the match.
Boosted by a typically fiery performance from De Klerk, the Sharks had much the better of the second half and while they were unable to get a try, Du Preez added a further four penalties to ensure they got just reward for their efforts.
With the visitors ahead 25-21, Saracens formed a powerful driving maul which eventually saw 19-year-old Joel Kpoku go over for the winning score, with scrumhalf Ben Spencer adding a conversion and penalty to seal the victory.
In other results, the Northampton Saints condemned Wasps to a third straight defeat by beating them 36-17 in the Midlands derby.
Australian winger Taqele Naiyaravoro was at his destructive best as he grabbed a brace of tries to help the home side stay in the hunt for a fourth-place finish.
The Exeter Chiefs put in a massive second-half effort to come from a 19-12 half-time deficit and beat the Bristol Bears 31-29 and stay unbeaten thanks to a penalty try after the hooter.
Johan Ackermann’s Gloucester scored five tries to beat the Leicester Tigers 36-13, with wing Ollie Thornly scoring two, Harlequins overcame a stubborn Newcastle Falcons side in a 20-7 victory, and Bath ground out a 28-13 win against the Worcester Warriors.
Round 7 results:
Gloucester 36 Leicester Tigers 13
Harlequins 20 Newcastle Falcons 7
Bath 28 Worcester Warriors 13
Northampton Saints 36 Wasps 17
Saracens 31 Sale Sharks 25
Bristol Bears 29 Exeter Chiefs 31