Liverpool looked in danger of dropping points against the Baggies after Hal Robson-Kanu gave the home side a 15th minute lead but Mohamed Salah equalised with his 22nd league goal of the season.
But after spurning a number of glorious opportunities to take the lead, Alisson popped up in the West Brom box in the final minute to show the Liverpool attackers how to do it by heading home unmarked from Trent Alexander-Arnold’s corner.
Liverpool now find themselves in fifth position, just a point behind fourth-placed Chelsea and three behind third-placed Leicester City with two games remaining.
Alisson is now only the sixth goalkeeper to score in the Premier League after Peter Schmeichel, Brad Friedel, Paul Robinson, Tim Howard and Asmir Begovic.
The Brazilian goalkeeper paid tribute to his father, who passed on earlier this season, in his post-match comments.
“I’m too emotional, this last month for everything that has happened with me and my family, but football is my life, I played since I can remember with my father,” Alisson told Sky Sports.
"I hope he was here to see it, I’m sure he is celebrating with God at his side.
"Sometimes you are fighting and things aren’t happening. I’m really happy to help them because we fight together and have a strong goal to achieve the Champions League, because we have won it once and everything starts with qualification.
"So I can’t be more happy than I am now."
