However, a crumbling scrum, a yellow card, and spirited comeback by the Irish side saw them pull to within a point, but the GUINNESS PRO12 champions held for an important victory.
"It was an utterly brilliant performance from the team in the first half," said Townsend.
"I was pleasantly surprised with the lead we built up; at one stage I would have taken 6-3 considering the conditions.
"To be 30-6 up against a great Connacht side showed how well the players played.
"Some of the rugby we played in the first half was the best we've seen over the last four years."
"Connacht are a real top team and we had to make sure we were on our game and hold our concentration right to the last minute.
"The team really responded to the crowd towards the end of the game.
"They got behind the players when they had to dig in deep and having a 6,000 plus crowd tonight even when the game is on the TV just shows the fantastic support we have here at Glasgow Warriors."
The Warriors, who are missing more players due to the Rugby World Cup than any other club side, will now prepare for a trip to Thomond Park for a rematch of last year's GUINNESS PRO12 final.
"We have a week off which gives the players some time off but we will be looking ahead to Munster in three weeks' time," added Townsend.
"They have worked really hard and when they come back we know we have a really tough game against Munster, so we have to maintain that level of commitment."
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Guinness PRO12 Connacht News
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