Rowe scored when he was left unmarked to head home a left wing corner as the Shrimps’ weaknesses at set pieces that were so costly against Wimbledon seven days earlier, came to the fire again.
In a game of few chances it was the vital moment although the Shrimps can be justifiably angry at not being awarded a first half penalty when referee Will Finnie somehow failed to see goalkeeper Pontus Dahlberg rugby tackle Greg Leigh to to the floor in an incident that would have undoubtedly seen the home side reduced to 10 men.
Boss Stephen Robinson made three changes to the side that lost against Wimbledon with a first start for Scott Wootton and recalls for Alfie McCalmont and Wes McDonald.
Morecambe started on the front foot with a right wing corner flicked on at the near post, jest evading Anthony O’Connor.
Doncaster replied with right wing back Kyle Knoyle forcing a decent near post save from Jokull Andresson after running on to BenClose’s diagonal ball.
The best chance of the first half fell to Wes McDonald 31 minutes. he was played in neatly by Arthur Gnahoua but saw his effort well blocked by Dahlberg.
The biggest talking point of the game game three minutes from the break when Morecambe should have been awarded a penalty when Greg Leigh picked up the ball in the box only to be dragged down by Dahlberg for what looked an obvious spot kick.
Doncaster, with five defeats from six games before the game, started the second half on the front foot with Rowe seeing an effort superbly blocked by Wootton and the same player forcing a goal line clearance from Ryan Cooney after a well worked corner.
After a lull in the game Doncaster went close again when Ethan Galbraith tested Andresson with a shot from distance.
The home side finally got the breakthrough they were desperate for 11 minutes from time when Rowe was left unchallenged in the box from a corner to loop a header over Andresson and into the top corner.
Morecambe pushed for a late equaliser with Wootton volleying over from the edge of the box and before Dahlberg produced a fine save low to his right to tip away a well struck Cole Stockton volley that was heading for the bottom right hand corner.
Morecambe: Andresson, Leigh (Gibson71), O’Connor, Wootton, Cooney, McDonald (McPake 78), Diagouraga, McLoughlin, McCalmont (Phillips 57), Gnahoua, Stockton
Subs not used: Letheren, Jones, Wildig, Delaney
Doncaster Rovers: Dahlberg, Knoyle, Anderson, Williams, Close, Rowe, Smith, Hiwula (Cukur 68), Dodoo, Galbraith, Vilca (Seaman 79)
Subs not used: Jones, Olowu, Bostock, Barlow, Gardner
Ref: W Finnie.
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