After scoring a 12th-minute penalty, the 21-year-old striker set up former Chelsea winger Omari Hutchinson for Ipswich’s second eight minutes after the break.
Chelsea dominated possession but were wasteful and the video assistant referee (VAR) ruled out a Joao Felix first-half equaliser after a long check for offside.
Earlier, ex-Manchester City striker Delap powered in a penalty that he won himself after VAR judged that there was “sufficient contact” by goalkeeper Filip Jorgensen after the Ipswich man had dribbled past him.
Delap later capitalised on Axel Disasi’s poor back pass to set up Hutchinson to make it 2-0.
Ipswich’s win puts them above Leicester City into 18th and just one point behind Wolves in the table as they look to move out of the bottom three.
Chelsea have now lost consecutive matches following the goalless draw at Everton that ended an eight-match winning run in all competitions, and they remain fourth in the Premier League.
Enzo Maresca’s men are 10 points behind league leaders Liverpool – with Arne Slot’s pace-setters also having a game in hand – leaving a sustained title challenge looking unlikely.
