Cherries striker Pitman smashed past Dean Gerken on 73 minutes after the goalkeeper had saved brilliantly from Andrew Surman’s long-range effort.
Murphy had opened the scoring after 58 minutes, turning home a teasing Frank Nouble cross past Lee Camp for his sixth of the season.
The result ensures Mick McCarthy’s men are now unbeaten in seven and have not lost away from Portman Road since early September, putting them in a play-off spot.
Away side Ipswich started brightly and forced a succession of corners. In-form striker David McGoldrick had the game’s first shot on goal after seven minutes but his side failed to build on the early promise.
Bournemouth sprung into life after 10 minutes and should have gone ahead through Ryan Fraser.
Lewis Grabban squared for Fraser after good work from Josh McQuoid but the Scottish winger saw his goal-bound drive brilliantly diverted wide by Luke Chambers.
Fresh from two wins in a row and full of confidence the Cherries went close to opening the scoring once more after 21 minutes.
Fraser sped on to a calamitous back pass from Ipswich left back Aaron Cresswell but blazed his shot over the bar when clean through on goal.
The Tractor Boys’ goal was living a charmed life and two minutes later Gerken had to be alert to tip over a dipping Eunan O’Kane effort.
Gerken’s best save of the afternoon was a brave stop from Bournemouth top scorer Lewis Grabban who had found space in the box after a good pass from Surman.
Ipswich, who named an unchanged side for the fifth successive match, pushed forward towards the end of the half but a deflected Luke Hyam effort was as close as they got to seriously troubling Camp.
Hyam got on the end of a Murphy cross straight after the break and would have scored but for a vital interception from Elliott Ward.
After Murphy’s strike Bournemouth pushed forward and Fraser continued his duel with Gerken but came off second best once again after 65 minutes.
Pitman’s fifth of the campaign lifted Bournemouth and in an end-to-end tussle it could have gone either way and the home side thought they had nicked the winner with 10 minutes remaining.
Matt Ritchie’s deep cross was palmed into his own net by Gerken but referee Phil Gibbs adjudged the keeper had been fouled in his box by Tommy Elphick.
Pitman smelt another goal after 82 minutes but directed his glancing header just wide from substitute Marc Pugh’s cross.
Gerken stayed strong until the end though, keeping out further drives from Surman and watching a Grabban header fly over the bar in injury time.