A stunning early strike from Philippe Coutinho and a 73rd-minute goal by Raheem Sterling saw Liverpool to a vital victory that moves them one point behind their fifth-placed opponents and two shy of Manchester United in fourth.
"It was an outstanding win for us, very controlled," Rodgers said. "Of course, you have got to defend at times, in particular away from home against a very good side.
"But it was a wonderful win for us and I thought as the game wore on, if we had picked our passes a bit better we might have got in a bit more.
"But we got two wonderful goals, different types of goals, and were defensively very, very strong so it was an excellent win.
"Today was a huge win. To come here and win at any time, it is always a good victory if you can get a win here."
Liverpool have bounced back from a torrid start to the season, losing just one of their last 14 Premier League matches ahead of next weekend's Anfield encounter with champions Manchester City.
Rodgers praised his players for turning their early struggles around and he is relishing further pivotal fixtures over the coming weeks
He said: "The first period of this season was nothing like what we've been in my time at the club. We had to find a solution to that.
"We have restructured the team and organised the team in a different way, to get that solidity back and get the balance back both offensively and defensively.
"And the players' response has been absolutely magnificent; we have been playing two or three times a week now for the last four months.
"When this team is in the condition that it has been for the majority of the last two-and-a-half months, we relish every game that we play.
"We have got Manchester City and Manchester United to play at home, and Arsenal away. It was a big step for us to go three points behind [third-placed Arsenal], considering the start we had to the season."
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