Ireland Sevens star Andrew Smith helped Connacht keep their Investec Champions Cup hopes alive as they beat 14-player Bristol to finally open their account.
Smith scored the fourth try in a 27-10 bonus point Pool 1 victory at the Dexcom Stadium with Shayne Bolton, Jack Aungier and Caolin Blade having crossed earlier on a night when the Bears were a man down for 67 minutes after Josh Caulfield's dismissal for a stamp on Ireland prop Finlay Bealham.
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Connacht, looking for their first point of the campaign in their fourth game, got off to the perfect start when winger Bolton crossed with just seven minutes gone, and they were handed a further boost six minutes later when Bears lock Caulfield was sent off for a stamp on Bealham.
Fellow front rower Aungier doubled the home side's lead with 20 minutes gone and stand-off JJ Hanrahan added the conversion as England prop Kyle Sinckler headed for the sin bin for an offence during the build-up.
AJ MacGinty reduced the deficit with a penalty as Sinckler returned, but the Irish province went in at the break 17-3 ahead courtesy of scrum-half Blade's jinking run, although it took a last-gasp tackle from David Hawkshaw to prevent Harry Randall from dragging the visitors back into it.
Smith saw an early second-half try ruled out for a toe in touch after a lengthy review, but he was not to be denied and crossed from replacement fly-half Jack Carty's pass to secure the bonus point with Carty converting successfully.
Bristol centre Kalaveti Ravouvou was adjudged to have lost control of the ball as he touched down and the visitors made a late push during which they mauled the ball towards the Connacht line, but collapsed as the home side responded.
Sinckler spilled the ball inches out after a quick tap-penalty set up a late chance, but after Carty had kicked a late penalty, the Bears pack made the pressure tell as Connacht collapsed a maul and conceded a penalty try.
Glasgow defeat Toulon to make last 16
Two tries apiece from Huw Jones and Kyle Rowe helped Glasgow Warriors to a 29-5 win over Toulon and into the last 16 of the Investec Champions Cup.
Franco Smith's side had to win to guarantee their passage out of the pool stage and they landed a total of five tries to get the job done with a bit to spare.
Toulon threatened a comeback when Gail Drean scored early in the second half but Warriors hit back to win comfortably.
Glasgow welcomed back Kyle Steyn and Jack Dempsey from long-term injury and handed a first start to Max Williamson in the second row.
A much-changed Toulon selection saw Scotland scrum-half Ben White rested, although former Scotland back-rower Cornell du Preez was named among the replacements.