And Townsend is confident that a good run of results will see them achieve their target of a top four finish.
He said: "The players are delighted and the win helps boost us up the table a little more with eight games to go.
"We've got Cardiff at home next so we know that if we keep on winning we'll put pressure on those teams in the top four."
Glasgow's released Scotland players helped make up for a poor first half as they found themselves 12-6 down at the interval.
The two tries were scored by centre Alex Dunbar and stand-off Duncan Weir, who scored just eight minutes from time.
"At half-time we spoke about fronting up as we weren't listening to the referee on a couple of occasions and we didn't look after ball," Townsend added.
"We stepped up in the set-piece, and defensively we got a lot better. Gordon Reid performed a great turnover later on which illustrated how much we improved.
"We came out in the second half with much more resolve, determination and we were more direct which led to Alex's try.
"We did enough to win, but we put ourselves in a tricky situation after the first half.
"Alex played well and was always looking to win the tackle contest. His run was excellent, picking up the ball from Mike Blair who also played well on his return."
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