Derby leapfrogged opponents who had started the day in second after Martin seized on indecision from Tommy Smith to give his side a precious three points and inflict Ipswich’s first defeat in 13 matches.
The hosts, largely out-of-sorts, started the brighter and almost took the lead after just three minutes when Jay Tabb took advantage of a fabulous crossfield pass by David McGoldrick.
The midfielder’s shot from the edge of the area was parried by Derby keeper Lee Grant with Daryl Murphy’s rebound blocked by Cyrus Christie.
The home side were shading the opening proceedings and McGoldrick fizzed a shot just over after a sharp exchange of passes with strike partner Murphy.
Minutes later, Derby fashioned their first chance when Jeff Hendrick’s low goalbound shot was blocked by Tyrone Mings and Christie fired the rebound just over.
On 19 minutes, the visitors went close again as Johnny Russell curled a free kick just wide.
Clear chances were at a premium in a cagey first half although Murphy blasted wide after finding some rare space in the visitors’ penalty area just before the interval.
Five minutes after the restart, Ipswich had the home fans off their seats. A neat period of passing ended with Teddy Bishop unleashing a stinging drive from 25 yards that the diving Grant did well to push away.
Minutes later, the hosts had a big shout for a penalty turned down after Tabb’s cross appeared to strike the arm of Richard Keogh.
After an initial bright start to the second half by Ipswich, it was against the run of play that Derby took the lead on 57 minutes.
Christie’s long ball was hopeful and should have been dealt with but Smith’s header back was woefully short and Martin nipped in to clip the ball over the onrushing Bartosz Bialkowski.
On the hour mark, Ipswich almost hit back when Bishop’s cross was flicked on by McGoldrick but Murphy’s header was too tame to beat Grant.
At the other end, Bialkowski saved from Will Hughes after some great work by Russell before the same player found room to get his shot away but the Town keeper saved low down to his right.
Ipswich offered little in the final 20 minutes, until the game came back to life in injury time.
Eustace was sent off for a second yellow, after hauling down McGoldrick, before Grant saved Kevin Bru’s fierce drive and Noel Hunt just failed to turn the ball in at the far post following a goalmouth scramble.
It was the first time Ipswich had tasted defeat at Portman Road for almost five months but Derby just about deserved the three points as they stretched their own unbeaten run to five games.