Sammie Szmodics’s 38th-minute goal has given the Blues a 1-0 half-time lead against Fulham at Craven Cottage.
Town made two changes from the team which beat Chelsea 2-0 on Monday with Omari Hutchinson missing out due to a groin injury and Wes Burns dropping to the bench.
Hutchinson was replaced by Szmodics, while Ben Johnson came into the team at right wing-back. Otherwise, it was the same side that defeated Chelsea.
Fulham made one change from the 2-2 draw home draw with AFC Bournemouth on Sunday with Andreas Pereira, the subject of interest from Brazilian side Palmeiras, dropping to the bench and Tom Cairney coming back in and skippering.
With the game being played in very heavy rain - as was the case when the teams last met at Craven Cottage in October 2001 when the match ended 1-1 - the home side saw most of the ball in the early stages.
Town, wearing their all pink third kit, made a break through Nathan Broadhead and Szmodics, playing in Hutchinson’s right-sided role, but the former Blackburn man was crowded out.
On five, Antonee Robinson’s deep cross from the left dipped over Christian Walton’s bar with the keeper carefully watching it on its way.
Four minutes later, after Liam Delap had won a free-kick, Leif Davis sent the ball dangerously across the box from the left after it had initially been cleared but beyond his teammates.
Fulham had dominated possession in the first quarter of an hour but the Blues briefly began to see more of the ball with the home side committing a number of fouls to stop them breaking, although their supporters were less than impressed with a couple of referee Darren Bond’s decisions.
However, it was the Cottagers who created the game’s first real chance in the 20th minute. Following a free-kick which had been half-cleared, Cairney sent in a cross from the left which Raul Jimenez headed goalwards but Walton saved sharply down to his right.
Within a minute, Alex Iwobi nutmegged Johnson and brought the ball into the left of the area before hitting a shot which was deflected behind by a covering defender.
In the 27th minute, Davis was shown the game’s first yellow card for sending Harry Wilson flying after the Wales international had exchanged passes with Jimenez and was bearing down on goal. The Whites fans called for a red card but referee showed only a yellow, which was the right decision. From the free-kick, Joachim Andersen headed straight into Walton’s arms.
Fulham continued to keep the Blues pinned in their own half and on 36 Robinson and Iwobi exchanged passes into the left of the box but Johnson did well to cut out the US international’s return ball before being clattered by Wilson.
As against Chelsea on Monday, Town had resolutely withstood Fulham’s pressure and in the 38th minute they took the lead.
Broadhead wafted a cross from the left towards the far post, Robinson nodded against his own bar under pressure from Johnson, Calvin Bassey scuffed his clearance straight to Szmodics, who slammed his fourth goal of the season - all away from home - into the net sending the Town fans at the other end wild.
Fulham set about getting back on terms and Broadhead picked up a yellow card for a foul on Cairney just inside the Town half.
Following a 44th-minute corner, the ball was cleared to Wilson on the edge of the box but his volley was blocked. Following the subsequent flag-kick, the ball was returned into the box and Walton claimed confidently in the air to cheers from the Town support behind his goal.
As the fourth official indicated one additional minute, Davis was sent away on the left but his low cross was beyond Delap.
The first half had been more of the same from the Blues. Solid defending restricting the opposition to few real chances and swift breaks from which Szmodics bagged his first goal since netting in the 2-1 win at Tottenham in November, also wearing the pink shirt.
Like their West London counterparts Chelsea earlier in the week, Fulham had seen a lot of the ball but with Walton only forced to make one serious save.
Another similarly resilient performance from the Blues in the second half and Town could be celebrating back-to-back Premier League wins for the first time since January and February 2002.
Ipswich: Walton, Johnson, O'Shea, Woolfenden, Greaves, Davis, Morsy (c), Cajuste, Szmodics, Broadhead, Delap. Subs: Muric, H Clarke, Burgess, Townsend, Phillips, Taylor, Burns, J Clarke, Al-Hamadi.
Fulham: Leno, Castagne, Diop, Andersen, Bassey, Robinson, Lukic, Cairney (c), Wilson, Jimenez, Iwobi. Subs: Benda, Cuenca, Sessegnon, Pereira, King, Smith Rowe, Traore, Godo, Muniz. Referee: Darren Bond (Lancashire). VAR: Paul Tierney.