Six minutes before the break, the winger used his pace to beat Keith Doyle down the right flank, and his cross was fired home by Stuart Byrne.
It was a second goal in as many eircom League games for Byrne, who scored Shels’ late equaliser from the penalty spot against UCD nine days ago.
And Baker, who returned to Shels after a year in the Major League with New England Revolution, fired Shels’ second 10 minutes from time, catching Rovers keeper Russell Payne on the hop with a surprise strike after Glen Crowe’s lay-off.
It could all have been so different for Roddy Collins’s Rovers, who were left to rue Stephen Gough’s penalty miss midway through the second half.
Referee Alan Kelly caused consternation in the Shels ranks by pointing to the spot after 64 minutes for a perceived handball by Colin Hawkins.
However, Gough sent his kick high over Steve Williams’s crossbar, and with it went Shels’ hopes of upstaging the title favourites.
Rovers’ night ended in further acrimony with manager Collins sent from the dug-out after incurring the wrath of referee Kelly.
Shamrock Rovers: Payne, Gough, McGuinness, Gavin, Doyle (McGovern), McCourt, McDonagh, Caffrey, Rutherford, Molloy, Feeney.
Shelbourne: Williams, Heary, Hawkins, Rogers, Crawley, Baker, Crawford?, S. Byrne, Moore (Cahill), Crowe, Byrne (Harris).
Referee: A. Kelly (Cork).