Liam Manning paid tribute to Rob Dickie’s eye for goal after the centre-back’s 73rd-minute strike settled an undistinguished Anglo-Welsh derby.
The tall defender’s glancing header from a Joe Williams chip into a crowded penalty area ended a run of four successive defeats for Bristol City and created a nine-point gap between themselves and the Championship relegation zone.
For opponents Swansea, that gap is only five points and they will need to add a cutting edge in the final third of the pitch to avoid dropping into trouble after dominating possession in the first half.
Robins head coach Manning hugged members of his coaching staff at the final whistle, clearly relieved after his team had been booed off at the interval.
He said: “We had to stop our poor run and we were never going to do that with flowing attractive football.
“I was pleased enough with our patience after a cagey first half and from then on it was a really solid team performance.”
“Rob Dickie is a huge player for us in both boxes. He is like a magnet for the ball when crosses come in.
“Being massive helps, but he also has the ability to hold off his marker and take up dangerous positions in front of goal.
“The message to the players before the game was to live in the present and not worry about past results or the future.
“But of course four successive defeats leave a mark and it was important to get a result to boost confidence again.
“I’m pleased with the clean sheet, particularly after a game at Ipswich in midweek in which we did most things right only to concede twice in the closing stages.”
Przemyslaw Placheta wasted Swansea’s best chance on 57 minutes, shooting badly wide at the far post from a Ronald cross.
Head coach Luke Williams insisted he was not looking at the bottom positions in the table.
“I didn’t see a team out there who are drifting or in any way dropping into trouble,” he said.
“I saw a side who controlled the game for much of the time and if the players can add better decision-making and greater coolness in front of goal we can finish the season really strongly.
“We paid for switching off at a set-piece and it was one of a few key moments in the game that cost us.
“Placheta needed to show more composure with his chance and get the shot on target. If we had scored then, I’m sure the least we would have come away with was a point.
“We dominated possession because Bristol City dropped deep when we had the ball. That made them difficult to unlock at the back and we needed to be better with our final ball.”