It was hard not to feel sorry for Rovers' injury-ravaged squad who, having been thumped 6-0 at home to Ipswich in midweek, then lost the services of Ryan Burge ahead of this clash and the influential James Coppinger during the pre-match warm-up.
Sean O'Driscoll was only able to name four substitutes at the Liberty Stadium - a reserve goalkeeper and three centre-halves - but even the latter trio could not have prevented what was essentially a training ground exercise for Swansea in the first half.
Scott Sinclair notched his 19th goal of season and Ashley Williams added a deserved second just before the break.
Rovers tightened up and prevented Swansea from having it all their own way after the break, but Luke Moore still managed to add another to move the Welsh outfit up to third in the Championship and inflict a seventh league defeat in eight games on the visitors.
No-one could deny Brendan Rodgers' side all three points as they racked up a total of 15 shots and 11 corners compared to zero from Doncaster on both accounts, with only a mixture of wayward finishing and brave defending keeping down the scoreline.
The writing was on the wall for Doncaster before the game had even got under way and the size of their task was realised as early as the sixth minute as Sinclair opened the scoring.
Nathan Dyer found Angel Rangel and the Spanish full-back burst into the area before squaring the ball to the former Chelsea man who converted from close range.
Swansea were playing the kind of free-flowing football the Liberty Stadium has become accustomed to over recent years, Rangel and Stephen Dobbie next to go close as the hosts looked to put the game to bed.
Dyer's exquisite lob in the 19th minute appeared to have doubled their advantage only for the impressive Sam Hird to clear off the line.
Sinclair, Moore and Rangel all tried their luck as the visitors continued to be overwhelmed, particularly down the right flank.
To their huge credit, O'Driscoll's side - which included debutants Jason Euell and Franck Moussa - looked to try and play their natural passing game when given any opportunity.
But it was only a matter of time before Swansea grabbed a second and it came in the 39th minute as Williams followed up his parried shot to head home the rebound.
Joe Allen still had time to go close before the curtain was drawn on a first half in which Doncaster failed to register any attacking threat.
Despite a continued lack of presence in the final third, Rovers managed to halt City's obvious dominance after the restart.
Neil Sullivan was forced to make his first save of the second half as late as the 70th minute, tipping over Dobbie's effort.
But it was game, set and match eight minutes later as substitute Darren Pratley set up Moore who fired home a third high into the middle of the goal from the edge of the area.