Johann van Graan’s side continued their unbeaten run with their first win at the Scotstoun Stadium since 2016, pushing their points tally to 27 points for an 11-point lead over the second-placed Scarlets.
An excellent performance by Damian de Allende and some good work in the last 20 minutes by the Munster side in general saw them pull away from Glasgow to ensure the victory.
The win contributed to a clean sweep for the Irish teams in the competition as their Guinness PRO14 dominance continues.
Leinster, meanwhile, continued their search for a fourth consecutive title with a 40-5 win over the Cardiff Blues, while Ulster also stretched their unbeaten march with a close 26-24 victory against the Scarlets – allowing them to pull further away at the top of the Conference A standings.
Leinster tops the conference on 35 points with seven wins from seven, while Ulster are two points behind after winning all of their matches but with fewer bonus points.
Ulster are, however, a massive 20 points ahead of the third placed Ospreys, who have 13 points this season.
In Belfast the Scarlets were left rueing missed kicks at goal as Ulster held on to take the victory, while Leinster looked classy as they continued to cruise through the competition.
Connacht, in turn, defeated Zebre 47-12 in Parma to move into third place in Conference B. They now trail the Scarlets by one point.
Sean O'Brien scored in his first game in two years for the province, turning the tide in the Irish side’s favour.
In the other game, a last gasp try by Dewi Lake gave the Ospreys a hard fought 24-22 win over Benetton to end the Welsh side’s three game losing streak.
The late try was preceded by a stunner by scrumhalf Shaun Venter, who scored a crucial five-pointer with time running out to give the Welsh side a chance, and Lake took it to break Italians’ hearts.
Guinness PRO14 Round 7 results:
Ospreys 24 – 22 Benetton
Zebre 12 – 47 Connacht
Leinster 40 – 5 Cardiff Blues
Ulster 26 – 24 Scarlets
Glasgow Warriors 13 – 27 Munster