Akinfenwa shocked the Trotters, who had captain Gary Cahill sent off for a terrible challenge before half-time, with two first-half goals.
The Town striker opened the scoring with a 22nd minute penalty and he doubled the League One club's lead six minutes later with a header from Adbul Osman's cross.
Bolton defender Cahill was then dismissed for a dreadful challenge on Giles Coke.
Substitute Kevin Nolan did pull one back late on for the hosts, but it proved no more than a consolation on a poor night for Gary Megson's side.
The Trotters boss made five changes from the side which was sunk by Michael Owen's late winner at Newcastle three days earlier.
But one of those, Danny Shittu, nearly gifted the visitors a dream start after just 40 seconds when the big defender slipped to let in Akinfenwa, who shot tamely at Jussi Jaaskelainen.
Debutant Shittu nearly made amends for his poor start, but his acrobatic volley struck the post on 10 minutes and the former Watford man then headed wide eight minutes later.
Town were ahead moments later when Andy Holt's cross struck Gavin McCann's hand and referee Graham Laws pointed to the spot.
Akinfenwa made no mistake from the spot, sending Jaaskelainen the wrong way and the Finnish shot-stopper was again picking the ball out of the net when the forward headed home on 28 minutes.
Coke nearly added a third for the Cobblers, before Cahill added to Wanderers' woes with his reckless lunge on the Town midfielder.
Joey O'Brien thought he had given Bolton a lifeline in first-half injury time, but his 25-yard free-kick was superbly turned away by keeper Mark Bunn.
Megson threw on substitutes Nolan and Kevin Davies in a last throw of the dice on 64 minutes. The two combined with eight minutes remaining when Nolan ran onto Davies' flick-on to lob Bunn.
And Wanderers thought they had sent the tie into extra time when Heidar Helguson turned in late on, only for his close-range effort to be ruled out for offside to complete a miserable night for the home side.