A brilliant brace from Owen Garvan and Kevin Lisbie's first goal in 11 games gave Ipswich a comfortable win.
Jonathan Walters hit the post before Garvan opened the scoring with a crisp volley from the edge of the area.
Garvan then delivered a sucker punch to Argyle three minutes before the break as he rifled in an unstoppable drive.
Lisbie made it 3-0 before Craig Cathcart headed a late consolation for Plymouth, but the visitors finished with 10 men after David Norris saw red.
Plymouth boss Paul Sturrock: "We were not at the races when the other team had the ball.
"One or two of them out there had their slippers on. Our performance had lethargy in it and I will check my ProZone, which will give me a run-down of where we went wrong.
"We finished up playing tippy-tappy in the back four. My players decided to play first, and defend second."
Ipswich boss Jim Magilton: "Plymouth is a tough place to come and they made it tough for us today but I thought it was a terrific performance from the whole team.
"We started brightly and Owen Garvan got two great goals for us, after good play in midfield, which put us in a fantastic position going in at half-time.
"We got a bit sloppy at times and gave the ball away too much at the end, but all round I thought it was a terrific display."
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