With the game finely poised McCombe gave the visitors the advantage two minutes from time when he nipped in front of his marker to head a Sam Morsy corner past Barry Roche.
Pope made things safe two minutes into injury time with a goal from close range after the Valiants took advantage of Morecambe pushing bodies forward for an equaliser.
Vale took the lead with less than a minute on the clock. The ball was played forward from the kick-off and Louis Dodds forced an early save from Roche but the ball rebounded into the path of midfielder Morsy who made no mistake from the edge of the box.
Morecambe levelled after 32 minutes with last term's top scorer Kevin Ellison opening his account for the season with an excellent individual goal. The striker took the ball on the right hand side of the box and cut inside to bear Chris Neal with a left-foot curler.