Colin Gregor was the star of the night scoring 20 points, including one of his side’s three tries as the Scots side moved into eight place in the table.
Gregor was making his first competitive start of the campaign and kicked two early penalties before Connacht were into their stride and although Paul Warwick scored with a penalty kick Glasgow were on the front foot and after Johnny Beattie had scooped up the ball from the base of a scrum to Graeme Beveridge, whose pass was perfectly delivered for full-back Graydon Staniforth to romp in under the crossbar, giving Gregor a formality of a conversion.
Glasgow kept up the pace , but a combination of desperate defending and careless hands prevented them from adding to their lead until Gregor completed his first-half treble with a 40-metre thump on the stroke of the interval.
Play became disjointed in the second period with both teams trying to over-complicate their approach but it was the Warriors who settled quickest to effectively put the match out of reach.
A well-controlled pack surge enabled lock Dan Turner to reach the target at full-stretch, with Gregor gleefully maintaining his 100% record with the boot as he expanded the lead to 20.
But Connacht were not completely killed off and less than five minutes later they sneaked in for a touchdown from Andy Farley, goaled by Warwick. Gregor burst back into the limelight to convert his own try under the crossbar in the wake of a breakout from the home 22-area featuring Hefin O’Hare and Shaw.