Left wing-back Rowe turned up in the centre of goal to slide home from close range after Chris Martin headed into his path on 59 minutes.
And Paterson made sure of the outcome in stoppage time with a low right-footed finish from 12 yards.
It meant maximum points from their first three games for the Robins under new head coach Dean Holden, whose side move joint top of the table.
For Wednesday, it was a first defeat as they look to overcome a 12-point deduction for breaching spending rules.
The visitors carved out the better chances in a first half high on effort but low on quality.
The first fell to Kadeem Harris in the fifth minute but he was unable to control a Liam Palmer cross at the far post.
Nahki Wells fired over following a City free-kick, but Bentley was brought into action again on 29 minutes after a Harris run and shot.
Josh Windass shot wide after City had surrendered possession in a dangerous area and Wednesday finished the half strongly.
Windass put a first-time shot wide from a Kachunga cross as the interval approached with City having failed to manufacture a clear opening.
That changed six minutes after the break when Wells found space inside the box and his low cross was just beyond Andreas Weimann racing in at the far post.
Wednesday keeper Cameron Dawson then had to show quick reactions to parry Taylor Moore's glancing header from a Paterson free-kick.
Rowe had a shot blocked with City on top for the first time. Wednesday failed to heed the warning and the wing-back's goal followed moments later.
Wells fired over when he might have made it 2-0 and the visitors looked rattled. For the second time in the game Weimann just failed to connect with a low Wells cross.
Moore miskicked when presented with a chance following a corner and it was all City until Massimo Luongo broke down the right on 75 minutes only to be denied by a brave Bentley save.
But it was Paterson who had the final say for a City team playing with increasing confidence.