With both sides trying to preserve unbeaten records, Scotstoun hosted the biggest crowd of the season, and the home side delivered by posting five tries to underline their title credentials.
However, Connacht played their part, scoring three tries to keep within a score of the Scots until the pressure from Gregor Townsend’s side took its toll at the death.
Super defence from Danie Poolman and Ian Porter prevented a 13th-minute touchdown, but the Warriors took charge of the scrum. Three successive penalties ensued and with the Scots on the front foot, influential lock Tim Swinson broke and Stuart Hogg did the rest, escaping the cover to touch down in the left corner, with Duncan Weir adding the extras.
With the wind making it difficult for Connacht to gain any territorial control, Jack Carty provided the spark, setting up camp inside the Glasgow half with a super break, but it was his chip that ricocheted off the covering defence that allowed Dave McSharry to grab Connacht’s opening try, which scrum-half Porter converted.
A Weir penalty kept Scottish noses in front before they were gifted a try just before the break when Darragh Leader’s attempted clearance was blocked and scrum-half Henry Pyrgos won the race to the line. Weir’s kick put Glasgow 17-7clear.
It did not improve after the break when Connacht, failing to capitalise on the wind, allowed the Glaswegians to gain a foothold, eventually finding space out wide with Sean Lamont putting Hogg away for the third try.
Connacht finally gained some momentum and made it count when Carty skipped both Robbie Henshaw and replacement Fionn Carr for Leader to dive over in the right corner. Carty added the touch-line conversion.
However, the try-scoring hero’s knock-on immediately afterwards let Swinson put DTH van der Merwe in for a try that Weir converted.
Once again Connacht responded and a penalty try converted by Porter put them back in bonus point territory.
However, Glasgow pressure put led to an intercept try for centre Mark Bennett, who ran in from deep inside his own half.
Other Pro12 result: Edinburgh 20 Scarlets 20.
GLASGOW: Hogg, S. Lamont, Bennett, Downey, van der Merwe, Weir, Pyrgos, Reid, MacArthur, Murray, Swinson, Kellock, Harley, Fusaro, Ashe. Replacements: Russell for Downey (68), McConnell for Pyrgos (76), Yanuyanutawa for Reid (68), Bryce for MacArthur (68), Ryder for Kellock (49), Eddie for Harley (65).
CONNACHT: D. Leader, Poolman, Henshaw, McSharry, Healy, Carty, Porter, Buckley, Heffernan, Ah You, Swift, Muldowney, Muldoon, McKeon, Naoupu. Replacements: Ronaldson for McSharry (53), Carr for Healy (48), J. Cooney for Porter (72), White for Buckley (58), Delahunt for Heffernan (77), Loughney for Ah You (58), Kearney for Swift (48), Roux for McKeon (68).
Ref: Claudio Blessano (Italy).