Jewell on Monday revealed he would remain in charge of the Suffolk club having considered his future after Saturday's 2-1 defeat at Hull.
The Liverpudlian received the complete backing of owner Marcus Evans and his players, among many others, when weighing up his decision and opted to stay, although he acknowledged results must improve and quickly.
However, this result means Ipswich are winless in 11 league and cup games, still without a home victory and bottom of the table following Peterborough's fine home win over high-flying Huddersfield.
Ipswich took a deserved lead after 24 minutes through DJ Campbell's close-range effort but Theo Robinson capitalised on an error from goalkeeper Stephen Henderson to pull Derby level five minutes before the break.
Both sides had chances to win it but the visitors stole the points at the death when Nathan Tyson, who only climbed off the bench nine minutes earlier, pounced from close range from Conor Sammon's cross.
Ipswich came flying out of the blocks and Rams goalkeeper Adam Legzdins was forced into three saves inside the opening 10 minutes.
Legzdins denied Lee Martin inside a minute - with Andy Drury clearing the bar on the rebound - then tipped Aaron Cresswell's long-range effort around a post before thwarting Jay Emmanuel-Thomas from 12 yards.
Derby, who had drawn their last three games and were unbeaten in four, finally threatened in the 20th minute.
Michael Jacobs, making his first league start, unleashed a shot from 30 yards which was comfortable for Henderson.
It came as no surprise when Ipswich finally took the lead in the 24th minute.
Martin's ball into the box was bundled in by Campbell, scoring for the second time in three appearances.
Emmanuel-Thomas almost made it 2-0 on the half-hour but Legzdins produced a stunning save to tip his six-yard strike around a post.
Jake Buxton headed over a Paul Coutts corner in a rare attack for Derby before Ipswich were punished for another mistake five minutes before the break.
Henderson spilled a shot from Sammon and Robinson was on hand to tuck home the rebound, his third goal in four games.
Craig Bryson then fired wide from 12 yards as Derby finished the half on a high.
Legzdins continued his impressive night's work when he pulled off another fine stop to turn Cresswell's long-range effort away for a corner seven minutes into the second period.
The Rams went up the other end and twice threatened themselves.
First Sammon shot wide from 25 yards after Ipswich failed to clear Brayford's effort, before Jacobs cracked a shot from 25 yards which Henderson parried away.
Having been on the end of some sustained Derby pressure, Ipswich finally managed to break out and a shot from Martin, following a fine run, flashed just wide in the 62nd minute.
Legzdins frustrated Ipswich again with 17 minutes remaining as he kept out Emmanuel-Thomas' 30-yard strike before Coutts drilled a shot just over the bar.
Tyson then delivered a sucker punch to Ipswich and Jewell with the late winner.