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Both sides were defensively strong at the start of the match, but the home side managed to open the scoring after 20 minutes when Charlie Sharples burst through in the corner.
Gloucester seemed to grow in confidence as half time approached, and managed to extend their advantage when Bill Meakes gathered the ball from a James Hook chip forward before sprinting across the line.
Connacht's attempts to reduce the deficit after the break fell short until the pack forced their way over inside the final 15 minutes, earning a penalty try to get the visitors off the mark.
The visitors pressed hard in the final minutes as they tried to force a score-levelling second try, but the Aviva Premiership side got the turnover to make sure that they held on.
Gloucester will face the winner of the match between Exeter Chiefs and Newcastle Falcons later this month for a place in the final.