Vale's prolific marksman Tom Pope squandered a couple of early chances before Fleetwood went close to taking an eighth-minute lead.
David Ball fastened on to Junior Brown's pass and the striker's first-time shot was tipped just wide by the diving Chris Neal.
Ball got his revenge, though, in the 26th minute when he put the visitors ahead following Brown's free-kick from the right flank.
Alan Goodall headed Brown's far post delivery back across the six-yard box and Ball poked the ball just over the line.
Vale were all over the place after that and Alex Titchiner, Brown and Rob Atkinson all threatened to add a second goal.
That duly arrived six minutes before the interval when Damien Johnson's free-kick was headed in from eight yards by the unmarked Goodall.
Vale responded after the break and Louis Dodds should have pulled one back in the 53rd minute when he blazed over the top from eight yards.
But it just wasn't Vale's day and Jennison Myrie-Williams fired a 69th-minute penalty straight at Fleetwood 'keeper Scott Davies after the winger had been tripped by Dean Howell.