Liverpool, whose four goals were shared by England internationals Jordan Henderson and Daniel Sturridge, squandered leads of 2-0 and 3-2 before finally securing the points, overtaking Manchester City as the Barclays Premier League's top scorers with 70 goals.
Although irresistible going forward the fourth-placed Reds were again erratic in defence, conceding to their former midfielder Jonjo Shelvey before Wilfried Bony scored a brace.
Henderson was Liverpool's matchwinner against Swansea
Liverpool have shipped eight more than title rivals Manchester City and Arsenal and 14 more than table-topping Chelsea, but Rodgers is not prepared to revert to a cagey game plan.
"I think that's not our style," he said. "I worry always to play good football. I'm not totally satisfied with always grinding out results.
"It's the point of the season where it's about winning, that's what professional sport is about at this level - especially if you're up there challenging - but for us, I will always concentrate on performance.
"Ultimately I always think the consequence of performing well consistently is good results.
"This season shows that, I think. When we play well more times than not we get the win.
"Today we were not quite at our best but we scored four goals and won the game. It was a very, very important performance for us."
Sturridge, who opened the scoring by rounding Michel Vorm and added a rare header before half-time, is used to seeing his name on the scoresheet, but Rodgers was delighted to see Henderson joining him.
Liverpool 4-3 Swansea
The former Sunderland midfielder has been in fine form this season, but had scored just once in the league prior to this match.
"He showed great leadership, you could see him driving the team on," said Rodgers.
"The first goal was outstanding, and we've been talking to him about getting up there because in training his finishing is sublime.
"But what was really pleasing was his second. We're telling him to arrive in the box because he's got the legs and the energy to do it.
"That's where his goal came from; there was a terrific reaction save from his first attempt and he followed it in. It was a really important finish for us."