Rhodes got the crucial touch over the line as Luke Chambers tried to clear Grant Hanley's effort and although the ball rebounded in off keeper Stephen Henderson, the goal was later awarded to the striker, who has now scored in seven consecutive league games for Blackburn.
Rovers manager Michael Appleton included DJ Campbell on the bench for his improving side. On-loan Campbell was looking to face a side for whom he scored 10 goals in 17 games earlier this season, but he had to wait until the second half to join the action.
Midfielder Lee Williamson, who also joined Appleton's revolution this week, was left out of Saturday's Championship clash at Ewood Park.
For Ipswich boss Mick McCarthy, goalkeeper Scott Loach was absent with a sprained thumb, Henderson deputising in his absence. Also missing was midfielder Lee Martin with a hamstring injury.
The two sides cancelled themselves out in the opening stages although Blackburn goalkeeper Jake Kean did comfortably save a speculative Guirane N'Daw effort from 30 yards after 20 minutes.
Aaron Mclean should have done better with a close-range header following an Aaron Cresswell corner, but the striker failed to trouble Kean, while at the other end, Danny Murphy's shot was similarly wide of the mark.
There had been no shortage of effort but the lack of cutting edge had been more than evident in a lacklustre first 45 minutes as neither side had showed the quality required for a concerted push for the play-offs.
The game was crying out for a moment of inspiration but the battle of attrition resumed at the start of the second half.
A free-kick from Morten Gamst Pedersen floated into Henderson's hands as neither side could find the killer touch in front of goal.
And Rovers were ahead within four minutes of the striker's arrival. It was a messy goal in a messy game, but it did mean the Tractor Boys were compelled to go on the attack.
But it was Blackburn who came closest to adding to the scoreline with Rhodes spurning a great chance with his head from only six yards out with 18 minutes left.
Colin Kazim-Richards then went close as Appleton's side turned the screw in the closing stages, Rhodes again missing the target from six yards in the final minute.