Giannakopolous had fired narrowly wide early on, before Darren Bent showed his pace to cut inside Tal Ben Haim only to curl his effort wide from the edge of the box.
Shekfi Kuqi had an angled effort blocked by Jussi Jasskelainen after a mistake by Bruno N'Gotty, and then Khalilou Fadiga flashed a left-foot drive narrowly wide at the other end.
Ian Westlake headed over from Scott Mitchell's cross before Ricardo Vaz Te tried his luck after cutting inside but fired wide.
Vaz Te sent a volley off target before Kuqi's angled drive from a Kevin Horlock pass was palmed out by Jaaskelainen for Ben Haim to scramble clear.
An unmarked Bent saw his header from a Jim Magilton corner blocked on the line by a combination of Jaaskelainen and Fadiga as Ipswich ended the half strongly, with Westlake firing over and Danny Karbassiyoon having a firm low drive well held.
Bent and Kuqi missed chances for Ipswich at the start of the second half, while Pedersen twice threatened at the far post as he gave a hint of what was to come.
Bolton broke through on the hour when El Hadji Diouf found Giannakopolous behind the Ipswich defence, with Mitchell playing him on-side, and he coolly curled the ball beyond Kelvin Davis with the outside of his right boot.
Pedersen got his first five minutes later when Mitchell lost possession and Diouf played in the Dane, who raced into the area before crashing a low shot beyond Davis.
Westlake had an unconvincing effort blocked by Jaaskelainen soon after, before Bolton killed the game off with a third on 69 minutes when sub Kevin Nolan won the ball and fed Pedersen who fired home again from an angled position.
A minute later, sub Miller gave Town a glimmer of hope when fellow replacement Pablo Counago laid the ball back and he despatched it low beyond Jaaskelainen.
Miller went through again in stoppage time only for Jaaskelainen to block, and Mitchell couldn't turn the loose ball in, but that was Town's only other chance to score after Miller's strike.
In between, Bolton had threatened on the break, with Pedersen twice close to a hat-trick, first with a flick on a Diouf cross which lacked the pace to trouble Davis, and then a firm angled drive which the home keeper plucked out of the sky.
Ipswich have bigger fish to fry at the top of the Championship, reflected in the fact their attendance was down 10,000 on the match on New Year's Day against West Ham, but Bolton will look to emulate their run to the Carling Cup final last season in this competition.