Leeds conceded first, just as they had against Millwall, Derby and Forest, when Stephen Dobbie latched on to David Cotterill's long ball over the top to fire home in the 13th minute.
But Leeds fought back in the second period and just about edged a keen contest at Elland Road thanks to Bradley Johnson's volleyed equaliser in the 56th minute and Luciano Becchio's cool finish eight minutes later.
Grayson said: "That's three wins in a row, which is pleasing. We are making a habit of having to come from behind and I like us to win games from the front, but if the players want to put me through the mill every week and we keep on winning, so be it.
"We started the game well enough and they went ahead through a mistake. Swansea are a good footballing team who pass the ball with pace and quality so we knew they would be a hard team to beat.
"In the first half we tried to force the issue too much and needed to pass the ball better. We tried to bring our flair players into the game, which we did in the second half. We showed our resilience again and Shane Higgs made some good saves for us. He came in because Kasper Schmeichel has a foot injury which has worsened."
Source: PA
Source: PA