Quins had a great chance to stretch their lead at the top after nearest rivals Saracens lost to Worcester on Friday night.
But they will have kicked themselves back down the motorway after they had Gloucester in trouble a few times in the second half but could not get the tries to recover from an early setback.
Wing Charlie Sharples, full-back Jonny May and flanker Akapusi Qera grabbed Gloucester's tries, with fly-half Freddie Burns booting four penalties and a conversion.
As well as Chisholm's tries, Quins' other points came from fly-half Nick Evans' boot with three penalties and two conversions.
Elsewhere, two tries from Thomas Waldrom helped Leicester Tigers leapfrog Northampton into third place after a comfortable home 42-15 win over struggling Newcastle.
With Leicester wrapping up the four-try bonus point just two minutes into the second half, the result leaves Newcastle still six points adrift of London Wasps at the other end of the table.
Horacio Agulla, Niall Morris, Julian Salvi, Thomas Waldrom (2) and Billy Twelvetrees all crossed over for the hosts while teenager George Ford hit three conversions and two penalties.
Bath completed an Aviva Premiership double over West Country rivals Exeter with a 12-9 victory in a game where all the points came through penalties at Sandy Park.
It was a typical derby clash with little between the teams but the outcome meant a fourth home defeat for the Chiefs in the league this season, and the Devon side have to look back to January 1978 for when they last beat Bath.
Chiefs fly-half Ignacio Mieres kicked two penalties to give the home side a 6-0 interval lead but Bath counterpart Tom Heathcote levelled things up.
Mieres then booted his side back in front but Heathcote had the final word, his four successful kicks from four attempts securing the win for Bath.
Sarries' hopes of finishing top suffered a setback on Friday night as Worcester pulled off an astonishing 16-11 win at Sixways.
In the first half Sarries held an 8-0 lead and for a period of 20 minutes they battered the Warriors as the home side failed to secure any possession at all.
Incredibly Worcester did not concede any further points at that stage and they slowly but surely got into the match - and with Andy Goode kicking 11 points they pulled off a tremendous win against all the odds.
Schalk Brits and Andy Saull showed excellent handling skills to send Michael Tagicakibau away on an unopposed 30-metre run to the line as Sarries struck early.
Alex Goode, making his 100th appearance for the club, missed the conversion but was soon successful with a simple penalty and the visitors had an early eight-point advantage.
With the last movement of the half, a clearance kick from Brits was charged down. Worcester took their opportunity, Andy Goode's pass went astray but Alex Grove hacked on the loose ball to collect and score the try which Goode converted to give the Warriors a scarcely believable 10-8 half-time lead.
Saracens regained the lead after 46 minutes, The Warriors offended at a lineout and Alex Goode made no mistake.
Andy Goode then kicked a straightforward penalty to give his side a 13-11 lead going into the final quarter.
Worcester's all-action game harassed Saracens into frequent errors, with Andy Goode rewarding his side with his third penalty.
In Friday night's other game, Sale Sharks ran in six tries as they powered to a dominant bonus-point 46-34 victory over Wasps, who succumbed to their ninth consecutive Aviva Premiership defeat.
Sale scored three first-half tries through Sam Tuitupou (twice) and Dwayne Peel as they opened up a 25-14 advantage, with Nick Macleod adding the rest from the boot. Wasps' response came from three Elliot Daly penalties and a Dominic Waldouck touchdown.
The Sharks repeated the try-scoring feat in the second period with Andy Powell, Johnny Leota and Rob Miller all going over, although two late Joe Simpson scores made the score more respectable.