Two second-half goals in three minutes from Nicklas Bendtner and Laurent Koscielny broke the Championship side's resistance in the second leg of the semi-final which gave Arsenal a 3-1 aggregate victory and a place in next month's final at Wembley Stadium.
Arsenal skipper Cesc Fabregas added the third after 77 minutes and they will now meet West Ham United or Birmingham City who play the second leg of their semi on Wednesday with the Hammers 2-1 ahead.
The victory kept alive Arsenal's hopes of winning at least one of the four competitions they are still involved in this season and picking up their first trophy since the 2005 FA Cup.
Manager Arsene Wenger, who has now guided the Gunners to nine cup finals in 14 years in charge, praised his team's display.
"We showed great spirit, it was a mature, calm and patient performance and it was important not to concede a goal," he told reporters.
"We want to win every competition we are in and this team deserve to be rewarded for their outstanding attitude and spirit."
The mood at the Emirates became more and more tense as Arsenal wasted a succession of chances and Ipswich manager Paul Jewell was delighted with his team's performance.
"We stopped them from scoring for 90 minutes at Portman Road and for an hour here, even though we rode our luck a little bit. They were always going to have more possession, but my players were not disgraced," he said.
Koscielny scored the second when he powerfully headed home a corner after a rare mistake by Fulop and Fabregas made it 3-0 when he shot through Fulop's legs after a swift breakaway.
"He was sick, and concussed and has gone to hospital tonight" Wenger said. "We shall see how he is in the morning."
