Evans scored his first goal in 37 matches early in the second half after heading home when Vincent Pericard headed on Tony Capaldi's free-kick.
Nicky Forster had put Ipswich ahead by heading in Chris Casement's cross for his fourth goal in four games.
Evans set up Capaldi to level before winning a game which left Ipswich in 15th - their lowest finish since 1966.
Ipswich manager Joe Royle:
"I am angry. The performance was just not good enough and I expected more, especialy after we took the lead.
"I am disappointed for our fans, who have travelled a long way to see this.
"But we have got three or four out and we did not match Plymouth physically. We needed more strength and the players like Alan Lee give us that."
Plymouth: Larrieu, Connolly, Wotton, Aljofree, Hodges, Norris, Buzsaky (Pulis 78), Nalis, Capaldi, Pericard (Reid 78), Evans (Chadwick 78).
Subs Not Used: McCormick, Barness.
Goals: Capaldi 28, Evans 57.
Ipswich: Supple, Casement, De Vos, Naylor, McEveley, Peters, Brekke-Skard (Parkin 53), Garvan (Magilton 60), Westlake (Trotter 80), Currie, Forster.
Subs Not Used: Price, Krause.
Booked: Naylor, De Vos.
Goals: Forster 12.
Ref: B Curson (Leicestershire).
Play-off semi-final dates:
Leeds v Preston
(Elland Road, Friday, 5 May, 1945 BST)
Crystal Palace v Watford
(Selhurst Park, Saturday, 6 May, 1215 BST)
Preston v Leeds
(Deepdale, Monday, 8 May, 1945 BST)
Watford v Crystal Palace
(Vicarage Road, Tuesday 9 May, 1945 BST)
Play-off dates for other divisions to be confirmed