Mohamed Salah netted his 200th goal for Liverpool to cancel out Jean-Philippe Mateta's spot-kick before Harvey Elliott scored a stoppage-time winner to seal the three points.
Liverpool, who top the standings on 37 points from 16 games, have made a habit of scoring late goals in recent weeks, with strikes from Trent Alexander-Arnold earning a draw against champions Manchester City and a 4-3 win over Fulham.
"We plan before the games for that – to start well, to stay well and to finish well," Alisson said on Saturday.
"But this is football, it's an unpredictable game and sometimes everything that you are doing doesn't work for many reasons and you don't have time during the game to discover what is going wrong.
"You have to change quickly in mind and sometimes it's about passion as well. We had that at the end of the game, the last 20 minutes, a lot of passion from our players, a lot of intensity and we never gave up. We were rewarded for that with scoring two goals."
Liverpool's title credentials face a tough test in December, with their next two league games pitting them against Manchester United and Arsenal.
"We know that we have big challenges now in December, big opponents," Alisson said.
"But in the Premier League, all the games are important, they have the same value. What matters is the passion that you put into the games. And the next challenge that we have in front of us is the most important, so we go for that."
