Frampton, who before the game had scored just twice in the last four years, struck just after the half-hour mark and nodded home his second goal after the break.
Sammy Moore then scored with a fine strike from the edge of the box before Michael Smith added a fourth late on.
Kaid Mohamed, on his second debut for the Dons having re-signed on-loan from Port Vale, was tripped by Pompey goalkeeper Trevor Carson inside the area after 22 minutes. Carson was booked but redeemed himself by saving Harry Pell's penalty down low to his left.
But the Dons did take the lead in the 34th minute as Mohamed volleyed Callum Kennedy's inswinging delivery across goal and Frampton stabbed home.
Andy Barcham had Pompey's best moments in the second half, curling over and hitting a post but Frampton put the game to bed with his 74th-minute header.
Moore rifled in a 25-yard half-volley with eight minutes to go and Smith wrapped the win by firing past Carson in injury time.