Nicke Kabamba hit a first half brace before Barnet were reduced to 10-men following a second yellow card for Jack Taylor in the second half.
Pools could have added to their tally but managed to see the game out with relative ease and move back into the top half of the table and just two points off a play-off place after 18 games.
Check out Dominic Scurr’s player ratings from the impressive victory by scrolling down and clicking through the pages...
1. Ben Killip - 7
Third straight clean sheet but didn't have to work as hard for it as his previous two. Made one decent stop late on but was rarely tested otherwise. Photo: Mark Fletcher
2. Mark Kitching - 7
A solid display down the left side and got into some good areas without finding the killer cross. Photo: Mark Fletcher
3. Fraser Kerr - 8
The busiest of the Pools defenders covered things well at the back with some great blocks. Came close to scoring himself his 30-yard strike crashed back off the crossbar. Photo: Mark Fletcher
4. Michael Raynes - 8
A fairly comfortable afternoon as he dealt with what came his way with ease. Photo: Ian Randall