Shelton Martis scored the only goal of the game as Doncaster beat Ipswich for their first win in 13 league games.
Morris's header also ended Doncaster's goal drought at home, which had stretched to 325 minutes of football.
Earlier, David Norris missed a sitter from six yards as Ipswich struggled to make any real impact in the game.
The second half saw Rovers keeper Neil Sullivan save Darren Ambrose's volley and then opposite number Richard Wright kept out Martin Woods' ferocious drive.
Doncaster manager Sean O'Driscoll:
"We played how we've played in all the games so far - we didn't approach this any different.
"We got a goal, which was nice, and it was something to cling onto and something to fight for.
"We had a little bit of luck where we could have conceded two or three goals but all credit goes to the players."
Ipswich Town manager Jim Magiliton:
"It's a poor defeat because the last seven or eight games we've been very good but four or five players were below par today.
"We lacked quality in vital areas. I think we got a little bit bullied and overrun in midfield - I think they beat us in that department.
"We've got plenty of experience in there but it was just a lack of quality and a lack of know-how."
Doncaster: Sullivan, Mills, Martis, Hird (Spicer 57), O'Connor, Wellens, Stock, Woods, Chambers, Heffernan (Guy 76), Price (Taylor 83).
Subs Not Used: Hayter, Elliott.
Booked: Mills, Heffernan.
Goals: Martis 42.
Ipswich: Richard Wright, Volz, Naylor, Bruce, David Wright, Norris, Garvan, Shumulikoski, Quinn (Ambrose 53), Walters (Stead 54), Lisbie (Counago 70).
Subs Not Used: Supple, Balkestein.
Booked: Volz, Bruce.
Att: 10,823
Ref: Kevin Friend (Leicestershire).
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