The Hoops now move within seven points of Rangers at the top of the Clydesdale Bank Premier League.
Keane said that, while Rangers still had the upper hand in the SPL run-in, his team were going to Ibrox to win.
"Of course it's going to be difficult at Ibrox, they are doing well at the moment but the pressure is all on them. Sometimes it's better to be chasing because we have absolutely nothing to lose.
"There is still a long way to go but we will be going there to win the game."
Boss Tony Mowbray was happy with three points and a clean sheet and highlighted the showing of his young central defensive partnership.
"[Thompson and Rogne] were thrown in to do a job and kept a clean sheet and stood up to the physical task that was in front of them,” Mowbray said.
"Looking at the team Dundee United put out, they thought there would be a weakness there. They had strong, physical guys up front but they handled it well."
"Are we likely to have [Hooiveld and Loovens] back for next week? I don't know. They will both be chasing I would suggest.
"The bottom line is that they will only have a chance when they get their boots on and get on the training ground. The clock doesn't stop for anybody, we will wait and see."