That victory temporarily put the Scottish outfit up into third in the table before Munster's win over Edinburgh moved them back down into fourth.
And after overseeing such a fine response from his players, Lineen has called for yet more as the race for a RaboDirect PRO12 play-off spot heats up.
"I thought our desire and hunger were immense and ultimately I believe we got the win because we wanted it more than Ulster and refused to take second best," he said.
"We needed a response to the defeat by Leinster and the boys gave me one. If we can sustain that type of hunger and desire, it will stand us in excellent stead for the rest of the campaign.
"We had built up some real momentum going to the RDS for the Heineken Cup tie and we have to be honest and say we took a sore one.
"I think the other massive thing for us is that when you take a sore one you have to respond fast.
"But for me this victory shows the extra maturity we have in the squad and now we have take that on into Sunday's trip to the Dragons."
Glasgow's impressive run of results has also coincided with a lack of injuries in the squad, a fact that is not lost on Lineen.
"You know at some stage in the season you are going to get hit by injury, but so far we have been relatively lucky," he added.
"When you look back to this stage last season, we were decimated with injuries to several key players such as our skipper Al Kellock.
"So now we go to Dragons with the bit back between our teeth.
"We know how tough it will be down there, but if our attitude and intensity remains at the levels we showed against Ulster I will have no fears."
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