Tommy Smith tapped in the opening goal eight minutes from half-time before Ipswich were pegged back by Kieran Lee's smartly-taken goal.
But Green headed home Stephen Hunt's wicked inswinging free-kick to ensure the three points - even if their play-off dreams had ended seven days ago.
Wednesday just shaded the opening exchanges with Michail Antonio denied a certain goal by an excellent block from Luke Chambers after eight minutes.
Sam Hutchinson and Atdhe Nuhiu could not find the target from headers as Wednesday continued to make the most of the game's half-chances before Frazier Richardson sliced a chance wide after a quick free-kick involving Aaron Cresswell and Frank Nouble.
Then out of nothing, Ipswich broke the deadlock after 37 minutes. A sustained period of pressure saw the ball fall to Green on the edge of the box.
Rather than shooting, the loan midfielder played a smart pass to Daryl Murphy whose curling shot was initially well saved by Damian Martinez but the keeper was grounded as Smith tapped the rebound into the empty net.
Minutes later they could have doubled their lead. Murphy broke clear and beat both away centre-backs, Glenn Loovens and Oguchi Onyewu, but his powerful shot hit the inside of the post.
The visitors were only denied a deserved half-time equaliser by the expertise of Town keeper Dean Gerken who first produced a wonderful diving save to thwart ex-Ipswich youngster Caolan Lavery.
Then from the resulting corner, Antonio turned the ball goalwards from inside the six-yard area but Gerken was again equal to it in the last action of a first-half that got better as it went on.
With Ipswich now looking more comfortable resorting back to 4-4-2 after starting in an unfamiliar 3-5-2 formation, Murphy headed over from Cresswell's fizzing cross.
At the other end, Nuhiu again showed his own prowess in the air but he again directed Chris Maguire's long centre wide of the far post.
But the impressive Wednesday travelling fans did not have to wait long to celebrate an equaliser, which came 10 minutes after the restart.
Joe Mattock's low cross from the left was initially miscued by Lavery but it fell invitingly to Lee who calmly found the far corner of the net.
Wednesday were in the ascendancy and the impressive Maguire tested Gerken's handling with a low drive from 25 yards.
So it was slightly against the run of play that Ipswich regained the lead in the 67th minute.
McCarthy's two substitutes both made an impact, Paul Taylor fouled and Hunt sending in a devilish inswinging free-kick which Green flicked into the net.
With neither side having anything meaningful to play for, the second half drifted although Antonio was guilty of wasting two good chances from distance before Cresswell blocked Hutchinson's fierce drive.