Hull City manager Nigel Adkins believes his team are still in the mix for an end-of-season play-off place.
Kamil Grosicki grabbed both goals in the 14th and 49th minutes to leave the Tigers five points off the top six while the hosts were left firmly rooted at the bottom of the table 13 points from safety and virtually doomed to League One next season.
Hull missed out on adding to their advantage when a shot from Marc Pugh hit the post in stoppage time but the victory was all that mattered to Adkins.
He said: “We have come away from home and the importance was we needed to get the three points.
“I thought we started the game slowly but we scored an excellent goal. It was a good bit of play and was a good goal and what a wonderful run by Jarrod Bowen which led to the second goal.
“It’s about getting the result. We didn’t play great football but we picked up the three points which puts us within five of the play-offs with seven games to go.
“We have got to keep going and we have two home games coming up against Reading and Wigan which are going to be tough, but we have got to pick up the points and who knows what will happen?”
The Tigers took the lead following a slick move down the right involving full-back Todd Kane and Fraizer Campbell, with the latter laying the ball off to Grosicki, who fired past Bartosz Bialkowski.
The Polish international added a second after good work by Bowen.
Ipswich had the ball cleared off the line three times.
Ipswich Town: Bialkowski, Bree, Chambers, Nsiala, Kenlock, Chalobah, Skuse (El Mizouni 74), Nolan (Dozzell 18), Edwards, Jackson (Quaner 61), Judge. Unused substitutes: Gerken, Downes, Emmanuel, Knudsen.
Hull City: Marshall, Kane, Burke (McKenzie 74), De Wijs, Lichaj, Bowen, Batty, Irvine, Grosicki (Evandro 87), Pugh, Campbell (Martin 38). Unused substitutes: Stewart, Milinkovic, Long, Ridgewell.
Referee: J Brooks (Leicestershire).