Henry Pyrgos, DTH van der Merwe and Mark Bennett also crossed the whitewash as the Warriors registered a 39-21 home victory over their Irish visitors.
Connacht responded through Dave McSharry, Darragh Leader and a penalty try, but lacked the quality to seriously unsettle a Glasgow side who stay undefeated after four rounds of games - their 100 per cent record intact.
Few imagined when the season's fixtures were announced that both sides would navigate their first three games without tasting defeat.
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While Glasgow had been impressive, Connacht, often portrayed as poor relations of the Irish provincial game, overcame Newport Gwent Dragons, Edinburgh and champions Leinster to start in scintillating style.
This was the match when their hot streak would end though, with Glasgow dominant from the early stages, as only intense defence and poor handling kept them from opening the scoring in the opening quarter of an hour.
Home lock Tim Swinson had the home support out of their seats after 15 minutes when he burst through, only to be hauled down five metres short. The ball was quickly recycled and it looked as if Bennett was over, however referee Claudio Blessano said he was held up.
A series of scrums had Glasgow battering at the door before Pyrgos passed from the base for Hogg to dart over to open the scoring with a 19th-minute try that Duncan Weir converted.
Connacht soon pulled the scores level against the run of play as they easily cut through Glasgow's defence. Jack Carty grubbed a kick through and McSharry was sharply on the ball to go over. Ian Porter converted.
A Weir penalty after 30 minutes put Glasgow ahead, but there was a degree of good fortune when they pulled further ahead.
Connacht full-back Leader fluffed a clearance which Pyrgos charged down with relish. The scrum-half then gathered a difficult ball before going over for the try which Weir easily converted.
Starting the second half with a determined show of ball control, Glasgow went through the phases with great patience, dragging more and more of the Connacht cover into some desperate defence. When the ball was released in the backs it passed through a flurry of hands before Hogg broke onto the ball and scored his second.
It was then Connacht's turn to go through their phases in what was to be their best period of the match. When the ball came wide it was Leader who went over wide on the right to narrow the gap just before the hour.
From the kick-off, Glasgow attacked again, winning a scrum on the Connacht 22. Adam Ashe picked up at the base, handing on the ball to Pyrgos who deftly crafted a short pass to Van der Merwe on the reverse angle. The Canadian was through at pace, running over for the bonus try.
With Weir converting and adding another penalty a few minutes later the game seemed over. But Connacht powered into Glasgow's 22 and after a series of scrums, Glasgow conceded a penalty try, setting up Connacht for a possible late challenge.
Connacht were throwing everything at Glasgow and were forcing the ball into Glasgow's 22 when, with five minutes to play, Bennett intercepted a pass and dashed 70 metres for the score which ended any doubt over the outcome.
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