But the result was rough on Vale and their caretaker manager Dean Glover, whose side produced a storming second-half rally as they almost snatched a point.
Kirk opened the scoring in the 19th minute when he converted a near-post cross from Ian Henderson after good work from Poul Hubertz and the striker took his total to the season to eight, 13 minutes later.
Kirk has already equalled last season's goal harvest but his second goal was a simple affair, with all the credit going to an excellent link-up between Danny Jackman and Colin Larkin, who delivered the killer cross.
There was great action throughout, with Vale's top scorer Luke Rodgers, a constant menace. He almost set up strike partner David McGoldrick in the first half but McGoldrick's downward header was pushed over the bar by Mark Bunn.
Meanwhile, Kirk was denied a hat-trick after an excellent save by Joe Anyon when Henderson headed the ball back across goal into Kirk's path.
The first half ended with a terrific double save by Bunn to firstly deny Danny Whitaker's deflected shot and then a rising drive from Rodgers.
Vale scored the goal their positive approach play deserved ten minutes after the break when McGoldrick shimmied in the box before smashing a shot beyond Bunn.
That sparked the visitors even more and Bunn saved with his legs when substitute Shane Tudor burst clear while Rodgers saw a screamer cannon off the crossbar before hitting another snapshot which was saved by Bunn.
Hubertz broke away at the other end and almost sealed the points with a curling shot against the base of the post, but it was Vale that ended the game strongly as they desperately tried to snatch the point which ultimately eluded them despite intensive pressure.