The defeat sparked angry scenes in the crowd who chanted 'sack the board' and 'where's the money gone?'
Police and stewards had to move in at one point as tempers frayed and the directors' box looked in danger of being invaded by furious supporters.
The result, ahead of the international break, leaves Luton with just seven games left to try and preserve their Championship status, while Ipswich now look safe.
Resisting the temptation to make sweeping changes after Newell's Thursday departure, caretaker-manager Brian Stein showed just two differences to the 11 that started the 2-1 midweek loss to Hull.
In came 19-year-old Austrian striker Besian Idrizaj, signed on loan from Liverpool until the end of season, for his debut, while skipper Steve Robinson also returned.
Luton started predictably with plenty of energy and Keith Keane was first to test visiting keeper Lewis Price in the sixth minute with a low 30-yard effort.
A succession of corners then saw a David Bell flag-kick only half cleared in the 13th minute and, as the ball bounced off Jason De Vos, Clarke Carlisle rifled in a 15-yard left-foot effort that Price tipped over the bar.
The visitors offered little threat, but were almost helped by a blunder from Marlon Beresford five minutes later when the goalkeeper flapped at a deep Alex Bruce free-kick and, as the ball bobbled around the penalty area in front of the unguarded net, Keane cleared the danger.
That sparked the Tractor Boys on and they took the lead through a similar situation after a foul by Idrizaj on the right touchline in the 39th minute.
Gary Roberts curled the ball in for Bruce to hook against the bar at the far post and Lee - who bagged a hat-trick in Ipswich's 5-0 win in the reverse fixture earlier in the season - was on hand to nod home the rebound from close range.
Stein switched things around at the break as he brought on Chris Coyne for Lewis Emanuel and Warren Feeney for the disappointing Idrizaj.
The reshuffle didn't have the desired effect and it was Ipswich who made it 2-0 in the 62nd minute when Fabian Wilnis made ground down the right and crossed for Beresford to lose out to Jon Walters which allowed substitute Richards to net left-footed from six yards.
The goal sparked unrest in the home crowd and Ipswich looked likely to add a third until a late rally by the Hatters that saw Bell's 20-yarder saved by Price in the 86th minute before substitute Bjorn Runstrom headed Bell's free-kick wide a minute later.
| Click here to discuss this match on the messageboard |
| Match Photos | After Match Reaction | Seasons Results |