Eddie Howe's Bournemouth moved to within a point of the top of League One on the back of second-half goals from Lewis Grabban and Marc Pugh.
Portsmouth manager Guy Whittingham included three players making their debut in Therry Racon, Patrick Agyemang and John Akinde and for an hour they posed Bournemouth plenty of problems.
Brett Pitman struck the crossbar with a 44th-minute header for Bournemouth, but Portsmouth had enough chances to have created an upset.
Adam Reed twice went close for Portsmouth and Agyemang headed wide from six yards.
But once Grabban converted his 13th goal of the season in the 63rd minute from Josh McQuoid's pass, Portsmouth fell away.
Bournemouth's second came in the 77th minute when Pugh ran on to Pitman's pass to beat goalkeeper Simon Eastwood.
Eastwood made a great last-minute save to deny substitute Matt Tubbs when clean through a tired defence.