Quins were cruising at the break as scores from Andre Esterhuizen, Marcus Smith and Cadan Murley replied to Scott Cummings' early effort.
Glasgow dominated the first half hour of the second half with tries from Johnny Matthews and ever-present George Horne levelling the contest, before Horne's penalty took Warriors ahead.
But replacement hooker Riley took his chance from the back of a maul on 76 minutes to send Quins into a Champions Cup quar ter-final for the first time in 11 years.
"Whenever we're ahead, we seem to let the opposition in," said star man Smith. "That's something we're working on. We're still not where we want to be, but we've got another European knockout now, which is exciting.
"In the last two years we've fallen at this hurdle, so that's a monkey off the back."
Denne historien er fra April 07, 2024-utgaven av The Rugby Paper.
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Denne historien er fra April 07, 2024-utgaven av The Rugby Paper.
Start din 7-dagers gratis prøveperiode på Magzter GOLD for å få tilgang til tusenvis av utvalgte premiumhistorier og 9000+ magasiner og aviser.
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Ten-try Chiefs show Pirates no mercy
TEN-TRY Exeter inflicted the backlash from six successive defeats in their worst ever start to a Premiership season on a young Pirates side suffering their own problems in the Championship.
South America look to keep on building
AS Sebastián Piñeyrúa's historic six-year term as President of Rugby Sudamérica comes to an end, his replacement shows no signs of slowing down.
Scarratt excited by new pathway
ENGLAND centurion Emily Scarratt is delighted with the new women's BUCS programme which aims to provide a smoother pathway for young aspiring female players.
Baxter: I want to make things better
ROB Baxter will not be walking away from Exeter, the only club still looking for a Premiership victory this season, believing he can get the Chiefs back on track and he cannot bear the thought of anyone else doing the job.
Pearce walks in his father's footsteps
PADDY Pearce is living a dream after emulating his father and great-uncle by playing for the club he supported as a boy, Bristol.
New England group will cause uncertainty
SO JUST when we thought that everything was getting sorted between the RFU, the clubs and players, a number of new agreements and a new group raises its head.
Galthie turns his sights to the future
FRANCE head coach Fabien Galthie offered the clearest hint yet of Les Bleus' future on Wednesday, when he released 19 players back F to their clubs for the ninth and final Top 14 round before the international break.
Gilmore has tightened up our defence - Anderson
CAMERON Anderson has hailed the impact made by defence coach Jason Gilmore, below, since he arrived at The Stoop in the summer.
Ampthill given 11-try lesson in class from Bath
BATH secured a thumping away success in the opening match of their Premiership Rugby Cup campaign against Ampthill at Dillingham Park.
New faces take the plaudits for Saints
NORTHAMPTON handed out a thorough lesson to a tame Leicester team in this one-sided East Midlands derby to launch the Premiership Cup.
