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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Six-try Fiji prove too strong for Samoa
FIJI started their bid for a sixth Pacific Nations Cup title with a 42-16, six-try win over arch rivals Samoa in Suva on Friday
James will prove to be a star at Racing
HERE'S a little prediction that will either leave me with egg on my face or looking like Nostradamus come next June.
BBC will be covering all 32 World Cup games
WORLD Rugby CEO Alan Gilpin believes a groundbreaking partnership with the BBC will ensure a 'generational moment' for women's rugby is seized at next summer's World Cup.
Youngsters were quick to take their chances
Ben Jaycock caught up with England U18s assistant and backs coach Will Parkin
Rae: Good to see promotion back
WITH promotion a realistic possibility for Championship clubs heading into the new season it has created renewed excitement levels across the league.
Boulton's respect for game he loves
COLIN Boulton of Derby County stands astride the Himalayan peaks of Football League champions, the only uncapped goalkeeper to have been a permanent fixture throughout two triumphant campaigns.
Robertson needs to redress the balance
IT WAS a cheap shot, admittedly, but only a pacifist or a fool would spurn the opportunity to kick the New Zealanders when they're down. \"What's the difference between the All Blacks and an arsonist?\" your columnist asked a radio host during a breakfast broadcast in 1998, eventually breaking an unnervingly long silence with the punchline: \"No arsonist would lose his last five matches.\"
Ospreys are improving every season - Booth
TOBY Booth has his eyes on a prize for his ever-improving Ospreys this season and if he achieves his ambitious goal it will scratch an itch that has been with him for almost 20 years.
Rosslyn Park show Barnes how it's done
NATIONAL One Rosslyn Park illustrated their league superiority by dispatching their London rivals Barnes 52-12.
Move to Glasgow suits Schickerling
IT wasn't all that long ago that Patrick Schickerling was being ear-marked as a potential England bolter, a player who was set for an exciting and dazzling career on the international stage.
