Bournemouth had earned themselves a four-point advantage with a 2-0 success at Millwall on Sunday, but Mick McCarthy's men responded by going one better at Portman Road.
Tommy Smith converted from close range to give the home side the lead in the 31st minute, before the division's top scorer Daryl Murphy netted his 17th of the campaign just before the hour.
David McGoldrick rounded off the scoring in stoppage time as Ipswich kept pace with the leaders.
Two points and a place behind Ipswich are Derby County, who defeated beleaguered Leeds United 2-0 at Pride Park.
Will Hughes was influential in Derby's opener, driving in a low cross from the left that Alex Mowatt deflected into his own net shortly before the break.
And Derby doubled their lead two minutes after the interval when Jake Buxton headed in Jeff Hendrick's cross.
It extended Leeds' winless run to five matches, with Neil Redfearn's men just a point above the bottom three.
Mired further in trouble are Wigan Athletic, who lost 1-0 to Sheffield Wednesday after going down to 10 men.
Malky Mackay's side had ended a four-match losing streak with a 2-0 win at Leeds last time out, but Callum McManaman's dismissal and Atdhe Nuhiu's winner 13 minutes from time leaves Wigan second from bottom.
