The home side never looked back after taking a 3-0 lead in the opening 21 minutes to maintain their two-point advantage at the top of the table over nearest rivals Leicester.
Captain Paul Merson and England Under-21 full-back Matthew Taylor also got in on the scoring act with Lee Morris and Georgi Kinkladze replying for Derby as Pompey scored six goals for the first time in 11 years.
But it was Ayegbeni who stole the show with his all-round display, as he claimed his third goal in as many games to show why Portsmouth's manager Harry Redknapp was so keen to sign him on-loan from Israel team Maccabi Haifa.
Ayegbeni set up Merson for his second minute opener before scoring himself 13 minutes later after Taylor had retrieved Kevin Harper's cross at the far post.
Taylor made it three soon after, finishing off a move that began with Todorov on the edge of his own penalty area and only some wayward finishing prevented Portsmouth going further in front before the interval.
But Derby were a different prospect in the second half and threatened to complete an amazing comeback when Morris and Kinkladze scored to make the scoreline 3-2 with 23 minutes still remaining.
Morris fired home his seventh goal of the season on 57 minutes after Shaka Hislop had been unable to hold Kinkladze's shot before the Georgian reduced the difference further from the penalty spot ten minutes later after Warren Barton had been fouled.
But Todorov restored Portsmouth's two-goal cushion on 73 minutes with a neat finish from Ayegbeni's pass before the pair combined ten minutes later for the Nigerian to score a fifth.
Derby's misery was complete five minutes from time when keeper Lee Grant could only partially block Todorov's arrogant flick and the striker followed up with the rebound into the roof of the net.