Both sides came into this Severnside encounter in need of a win, having each gone three games in the Championship without victory.
Swansea’s need was considerably greater, as five defeats from their previous eight matches in all competitions had cost former head coach Sheehan his job.
The Welsh club identified Maritimo boss Matos as his successor and, while the details of his appointment were finalised, the ex-Liverpool development coach was at Ashton Gate to see the Swans in action.
His flight from Portugal meant he was not in his seat in time for kick-off and missed the opening goal, Mehmeti’s inswinging corner headed in by Dickie despite a touch from Swansea goalkeeper Lawrence Vigouroux.
That was just one of a series of early Bristol City chances and, although their opponents weathered the storm and created opportunities of their own, the Swans shot themselves in the foot.
The initial error came from Ronald who gave the ball away needlessly to Riis with a no-look back-pass, although Cameron Burgess saved his blushes with a goal-line clearance from Sinclair Armstrong.
But a ruffled Swansea backline could not navigate that period of pressure and, seconds later, Mehmeti’s deep cross was volleyed in at the back post by Riis.
That proved to be the pattern of the game as Swansea could have reduced their deficit on numerous occasions – Adam Idah and Liam Cullen squandering some of their best chances – only to be picked off by their ruthless opponents.
On one of the rare occasions Bristol City failed to punish their cross-border rivals, Armstrong was denied by a brilliant Vigouroux save low to his right.
But the hosts were clinical with eight minutes to go when Swansea committed players forward for a corner and were exposed by Bristol City.
The home side broke at pace with Mehmeti swivelling past two opponents and threading an excellent through-ball for substitute Hirakawa, who scampered clear and rolled his finish into the bottom corner to seal a comfortable win.
