The Warriors trailed 6-5 at the break as Craig Ronaldson slotted two penalties for Connacht to cancel out Mark Bennett's try.
But Glasgow shut out their opponents in the second half and triumphed thanks to Ruaridh Jackson's penalty to leave Townsend a happy man.
"A lot of players put their hands up today and guys like James Eddie and Fraser Brown coming off the bench did really well," he told the Glasgow Warriors website.
"Henry Pyrgos had a very good game, he was very smart in the first half when playing into the wind and Leone Nakarawa had an excellent game, carrying the ball very well.
"I think we were missing about 20 players so it just shows the strength of our squad but also the effort that was put in there to win.
"Connacht were missing players to injury but they don't lose anyone to international call ups so it shows we have quality players in order to cope.
"The conditions were really bad. It's hard when you're up at the back of the stand like us coaches to appreciate just how difficult the conditions are for handling. It's tough to play into the wind but handling is difficult with the wind behind you."
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