Paul Cook’s side deservedly went ahead in the 13th minute. Wes Burns rolled a low cross into the box and Macauley Bonne beat Pontus Dahlberg.
The visitors had a let-off when Burns charged through, only to be thwarted by an offside flag.
But the Tractor Boys bagged the second goal they had been threatening in the 31st minute, Lee Evans volleying home clinically.
Sam Morsy came close to a third just before the end of what had been a dismal opening 45 minutes from Rovers.
Rovers boss Wellens made a double change at the break, but it made little difference to the flow of the game.
A frustrating night for the visitors was summed up when Tom Anderson had to receive treatment after being whacked in the face by an acrobatic effort from Burns.
Evans then nodded home Ipswich’s third as he met Bersant Celina’s cross, before Bonne drove home a killer fourth.
Evans lashed home his third and Ipswich’s fifth in the 76th minute, before George Edmundson crashed home another.
Ipswich substitute Rekeem Harper thumped a post late on.
Ipswich: Hladky, Donacien, Edmundson, Burgess, Penney, Burns (Aluko, 77), Morsy, Celina (Chaplin, 77), Evans (Harper, 82), Fraser, Bonne. Unused substitutes: Holy, Woolfenden, El Mizouni, Norwood.
Doncaster Rovers: Dahlberg, Knoyle, Williams, Anderson, Rowe, Gardner (Vilca, 46), Close, Smith, Dodoo, Cukur (Barlow, 78), Hiwula (Olowu, 46). Unused substitutes: Jones, Seaman, Horton, Hasani.
Referee: C Brook (Sussex).