But in a remarkable finale, Sale fought back to collect two points as their hosts switched off following a 10-minute injury break.
Quins won their fifth straight game - their best start to a season since 1996 - and therefore remain top of the table.
Jeremy Staunton scored all 25 points for Leicester at a sunbaked Recreation Ground but still finished on the losing side as Bath won 26-25.
The Irishman could have won the game all on his own but at the death, given a 45-metre penalty to win the game with the clock at zero, he pushed the ball wide.
It was his only kicking failure all afternoon.
Instead it was Bath's 19-year-old Academy fly-half Tom Heathcote who stole the limelight, coming on at half-time for Sam Vesty and landing a touchline conversion before adding two penalties to snatch victory.
Gloucester extended their unbeaten home record to 22 games as a penalty from replacement Freddie Burns saw them edge a thrilling 33-10 encounter with London Irish at Kingsholm.
The Cherry and Whites had looked well on course for victory after opening up a 23-10 advantage late in the first half thanks in part to a Tom Voyce score and a penalty try.
But Irish, who had claimed the opening try through Alex Gray in the first minute, hit back as Topsy Ojo and Steve Shingler went over to help them establish a 27-23 lead.
Hooker Darren Dawidiuk responded with the hosts' third try while Tim Taylor kicked 15 points, but it was a penalty from Burns which eventually sealed the win after Exiles full-back Tom Homer, who racked up 15 points of his own, had tied the scores with his third penalty.
Reigning champions Saracens made it four wins out of five this season and maintained their unbeaten run away from Vicarage Road with a 17-13 win over Exeter.
But hosts Exeter kept battling until the final whistle in search of a losing bonus point.
After a very fast opening half in the Devon sunshine at Sandy Park, Saracens led 10-6 after Owen Farrell broke through for the only try, which Charlie Hodgson converted.
Farrell then took over the kicking duties and, kicking into a light breeze, landed a penalty while fly-half Ignacio Mieres was on target with two of his three attempts for the Chiefs.
The former England and British & Irish Lions half-back scored what looked like being the only points of the second half as he converted his own touchdown.
But with time up on the clock the Chiefs took a quick tap penalty through replacement scrum-half Kevin Barrett and number eight Ritchie Baxter went over the line, with Mieres adding the conversion for the bonus point.
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The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
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The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.