The former Springboks Under-20 skipper Stander came off the bench in the 13-6 RaboDirect PRO12 defeat against Scarlets last time out but he made sure he took full advantage of his starting berth this time round with two tries.
Ronan O'Gara contributed 11 points while Tommy O'Donnell and a penalty score provided the other scores for the home side - Duncan Weir kicking the Warriors' only points.
Weir drew first blood for the visitors when he kicked a third-minute penalty after Munster were penalised for not rolling away at a ruck.
But Munster didn't take long too get themselves in front. South African flanker Stander enjoyed the perfect possible opening on his first start for Munster by crossing.
Ronan O'Gara kicked the extras and the home side were 7-3 to the good before minutes later the forwards from both sides broke out in a spot of fisticuffs.
As the half approached the midway point the Warriors thought they had got themselves ahead. After an incisive break by Sean Lamont the ball went wide and D.T.H van der Merwe touched down but the television match official ruled that he had been in touch.
Warriors fly-half Weir snatched at a half-chance to kick a drop goal and reduce the margin after 18 minutes.
O'Donnell had a significant hand in Munster's first score and he galloped over for a try of his own in fine style after 23 minutes.
Fly-half O'Gara couldn't miss the conversion from under the posts and after the Warriors' promising start they found themselves 14-3 down.
O'Gara's right boot was responsible for three more points as the half-time whistle beckoned, the fly-half himself obstructed by Michael Cusack to be given the penalty chance.
And the game was all-but over before the half-time whistle. A Glasgow pass went astray and Stander picked up and backed himself to race over from distance and touch down in the corner, O'Gara converting expertly from out wide for a 24-3 interval lead.
Munster thought they had got the first score after the break when hooker Mike Sherry went over in the right corner but he was adjudged in touch by the TMO thanks largely to a try-saving tackle from Rob Harley.
However the home side got the bonus-point score with some typical Munster pressure at scrum-time delivering a penalty try. O'Gara added the extras to put the icing on the cake of a comfortable victory.
|Munster Rugby Score Card|
|Glasgow Warriors Score Card|