That win means the Warriors will be guaranteed a play-off berth with either a win or a draw in their game against Connacht on May 5.
And Lineen insisted the praise for the nail-biting victory was two-fold, both for van der Merwe and his timely try and his side's fighting qualities.
"It wasn't the prettiest game by a long shot, but we stuck in really well and got the result we came for," Lineen told www.glasgowwarriors.org.
"It puts us in a good position in terms of qualifying for the play-offs, and we're looking forward to seeing Firhill really busy on 5 May for what has all the ingredients to be a momentous night in the club's history.
"It was fantastic for DTH to come back into the side and hit the ground running with a really well taken score. Credit to Henry Pyrgos for putting him away, and then to DTH for backing himself and getting the try.
"I was very impressed again by the passion and commitment the whole team displayed throughout. We didn't produce anything like our best rugby, but we showed good maturity under pressure and won in a very difficult place.
"The support we had in the stadium was fantastic. Hopefully we can give them even more to cheer about on the 5th."
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