Pitman took his tally to 18 for the season with a goal in either half to give the Cherries, who have had a traumatic season, a convincing win.
Eddie Howe's side were handed a dream start when defender Joel Ward beat the static Morecambe keeper Barry Roche to Danny Hollands' dangerous inswinging corner.
And the Cherries should have gone 2-0 up just before the half-hour when Roche saved superbly from Pitman and then got up to make an excellent second save from Josh Goulding's follow up.
His blushes were spared after 35 minutes though by Liam Feeney who made it 2-0 with a superb strike past Roche and then Pitman opened his account just before half-time with a superb goal on the turn.
The visitors played with flair in the second period with Josh McQuoid and Jeff Goulding going close before Pitman capped a fine afternoon for the Cherries with his second in the 69th minute as he steamed in at the far post to slot home a left-wing cross.