Glasgow scored two tries in the opening four minutes yet had to hold out desperately in the final minute to beat their bogey team 29-25.
But Lineen was able to find positives in the match between two sides who could not qualify for the quarter-finals.
He said: "The most important thing was that we won and so kept up the winning momentum."
Focusing on the Magners League which Glasgow currently top, he said: "That is our side that will play during the Six Nations, and they now have the winning habit. We also have tonight's win up our sleeves ahead of the Dragons' return in April."
A feature of the team Lineen had put out was the number of fringe players who started for seven rested internationals.
Lineen praised young stand-off Ruaridh Jackson of whom big things are expected.
Lineen said: "Considering Ruaridh had only had that minute of rugby before he was injured in the first game if the season he did OK. He was rusty but he was trying things."