Connacht scored a try in either half from wing Mark McCrea and prop Nathan White but were always chasing their hosts who were after their maiden home win since moving from Firhill.
The game was preceded by an impeccably observed minute's silence in remembrance of Ulster player Nevin Spence and his father Noel and brother Graham who tragically died last weekend in a farming accident.
Warriors fans were given early evidence that this would be the match where they could start their Scotstoun victory tally when Scott Wight knocked over a penalty in the second minute.
The 26-year-old erred with his second attempt on goal but it was the strength of his boot which set up the game's opening try.
Off a free-kick deep in Glasgow's half, Wight launched a huge Garryowen which Connacht failed to deal with and scrum-half Kieran Marmion rushed to clear his lines.
But Warriors lock Tom Ryder swarmed over the 22-year-old, deflecting his kick into the path of prop Moray Low.
With Connacht's defence all at sea, the ball was shipped to Lamont on the right wing and he powered into the corner but from a tight angle Wight failed to convert.
A charged-up Lamont then set up full-back Murchie for a 50-metre score after Glasgow quickly spread the play from left to right.
Murchie fooled Connacht full-back Gavin Duffy with an inside swerve to dot down close enough to the posts for Wight to comfortably add the extras.
Connacht refused to submit to Glasgow's intent for the game to be played in the wide channels and conjured up a try from a direct grubber kick by fly-half Matthew Jarvis.
Wing McCrea had anticipated Jarvis' ploy and beat the covering Henry Pyrgos to touch down under the posts and his No.10 drove the conversion home.
Connacht had found their feet by now and sustained pressure from the Irish province gave Jarvis the opportunity to hit his first penalty of the night making it 15-10 at half-time.
The second half exploded to life with neither side being able to deal with the high ball leading to two quick-fire tries.
First Wight launched a huge up-and-under and when Connacht spilt the ball again Van der Merwe pounced for his third try of the season, Wight converting.
But straight from the kick-off Connacht repeated the trick on their hosts with Jarvis' hanging re-start proving too slippery for Al Kellock to handle and prop White strolled in for a try converted by its creator.
But Van der Merwe settled matters ten minutes from time when replacement Ruaridh Jackson passed to Murchie who fed the speedster for an easy run into the corner to seal the game.
|Glasgow Warriors Score Card|
|DTH van der Merwe||2||10|
|Connacht Rugby Score Card|