After an edgy first half in which Lewis Haldane struck the post for Vale and Brett Pitman did the same for Bournemouth, the game came to life after the break.
Pitman eased Bournemouth towards a comfortable win by opening the scoring in the 53rd minute after converting Rhoys Wiggins corner from 12 yards.
Bournemouth manager Eddie Howe sent on Connell as a 74th minute substitute and Connell responded by scoring twice in the next seven.
Connell's first came in the 75th minute with a lob from the edge of the area and his second came six minutes later from close range following a cross by Liam Feeney.
Feeney was involved again four minutes from time with a centre headed in by another substitute, Josh McQuoid.