On-loan Hearts forward Pollock's neat finish broke the deadlock in the first half before Hanlon opened his account for Rovers after the break.
The win leaves Robson's side just four points adrift of the top four while Pars remain in the relegation dogfight.
And basement side Airdrie, who are seven points worse off, could turn up the heat with victory over Livingston today.
Robson said: "I think the game plan worked perfectly. I think you can see the way we wanted to press them we were really aggressive with it.
"We looked electric at times, we looked so good at opening them up, especially on transition with the press. Finlay's been outstanding, it suits the way we play. He plays in that position, in between a striker and a winger and that's hard for especially a back four to pick up.
"If he wants to go to the next level and to the top, I've said to him, you have to run like that, you have to fight like that - the best players do."
Toothless Dunfermline haven't scored in eight of their last 11 outings and never looked like finding a way past Raith keeper Josh Rae.
The hosts went close to going ahead inside the first minute after Jamie Gullan crashed a free-kick off the bar.
Pars tried to make inroads at the other end but a hopeful Chris Kane shot from distance bounced harmlessly wide.
Pollock had a running battle with Jeremiah Chilokoa-Mullen even though the pair will be team-mates next week when they link up with Scotland Under-21s.
But Pollock was all smiles in the 22nd minute when he fired Raith ahead. The 20-year-old raced clear of Kyle Bene-dictus to get on the end of Dylan Easton's superb piercing pass and rounded Tobi O...