Ulster had piled on the pressure in the second half but had just two Ian Humphreys penalties to show for their efforts with the Glasgow defence holding firm.
And debutant David Lemi then fed Nathan for the crucial score as Glasgow made it four wins on the bounce at home.
Lineen said: "We got the win, what a fantastic result. The boys' determination was outstanding.
"I'm delighted that Duncan got the drop goal and put them out of range; I'm delighted for Troy scoring a great try and I'm delighted that David Lemi got through his first game in such wintry conditions.
"However, the match was frustrating at times and there were a lot of scrums, but we came through it and have another RaboDirect PRO12 win under our belts."
Lineen saved special praise for No.8 Chris Fusaro who replaced Ryan Wilson midway through the first half and enjoyed a fantastic match in the back row.
He added: "This is a tough competition and Ulster are very physical, but we faced up to them. Chris Fusaro came on and stole some beauties. He really is a star in the making."
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