With a trip to Heineken Cup finalists Leinster in the RaboDirect PRO12 semi-finals next on the agenda for Sean Lineen's side, the Warriors coach sensibly withdrew his injury-prone winger on the hour before No.8 John Barclay added gloss to the scoreline with ten minutes remaining.
It could yet be a season to remember for Glasgow who will move to the Scotstoun Stadium in the summer, but for Connacht a fine recent run came to an abrupt end.
The Irish province were looking for their fourth straight RaboDirect PRO12 victory which would have guaranteed their highest league placing of eighth - but Weir broke the deadlock on ten minutes to set the tone for the match.
Miah Nikora responded with an effort of his own moments later before Scotland international Weir then added another three points.
It was all a prelude to the main action however, as van der Merwe got himself on the Warriors' scoresheet to show the home faithful what they have been missing.
The winger benefitted from a neat interchange between Richie Gray and Stuart Hogg before crashing over on the left from close range just before the half hour mark.
Weir missed the conversion but the Warriors maintained their 11-3 advantage until the break.
The stand-off made amends when he slotted over a penalty eight minutes after the restart and the hosts could have added to their lead when van der Merwe went on one of his trademark mazy runs.
The South African-born winger jinked his way past three Connacht defenders before Frank Murphy dragged him into touch five metres from the line.
Weir kept up his impressive record with the boot by adding another three-pointer on the hour as ill-discipline put pay to Connacht's slim hopes of victory.
Paul O'Donohoe was sent to the sin-bin with 13 minutes remaining and they were duly punished when Barclay forced his way over the line from a scrum.
The visitors tried in vain to grab a consolation with George Naoupu denied inches from the line, but it mattered little to either side with the Warriors now turning their attentions to the RDS Arena, and results elsewhere giving Connacht their eighth-placed finish.
|Glasgow Warriors Score Card|
|DTH van der Merwe||1||5|
|Connacht Rugby Score Card|