They had to wait until the 84th minute for Scott Sinclair's winner, but Rodgers was purring afterwards having seen the Swans move three points behind second-placed QPR.
"I said to the players at half-time that they had to keep faith and they did. I thought our performance was outstanding, we showed courage and had to be patient and got the win with a terrific goal," he said.
"We controlled the majority of the game, Middlesbrough have good players and a good manager but we were outstanding in possession, we had chances in the first half which we didn't take but then we got the winner in the second half.
"We were a bit mentally fatigued in the week but we got back on track against a team that has picked up recently."