The 31-year old is on a three-month loan from QPR and has made a great impression at Portman Road with goals in seven of his 12 starts thus far.
Campbell gave Ipswich the lead in the 37th minute when he slotted home from close range before Daryl Murphy made it 2-0 five minutes into the second half.
The 64th minute saw Campbell wrap up proceedings when he converted form the penalty spot after Shane Lowry handled in the area to send the Tractor Boys to 20th on the table on the back of three wins on the trot.
Ipswich boss Mick McCarthy admits he is keen to keep Campbell at the club and is hoping to clear it up with R’s boss Harry Redknapp as soon as possible.
"I left Harry Redknapp a message the other day but I think he's got plenty on at the moment," he said.
"We can't do anything about it anyway. It'll run its course but other people will be interested because he's scoring goals.
"He wants to sign for a club permanently and we'd like to take him, but there will be mitigating circumstances."