Brighton were 1-0 down and seconds away from a painful home loss when Liverpool defender Andy Robertson kicked Danny Welbeck's foot in the penalty area.
Referee Stuart Attwell awarded the penalty in the 93rd minute after viewing the pitchside screen and Pascal Gross slammed home the spot kick to make it 1-1.
It was Brighton's second penalty after Neal Maupay previously fired a first-half spot-kick wide after the lively Aaron Connolly was sent tumbling following a clumsy challenge by Neco Williams.
Jurgen Klopp's team had a maddening afternoon with VAR as Mohamed Salah and Sadio Mane both had goals chalked-off for offside.
Liverpool skipper Jordan Henderson and veteran James Milner were highly critical of the video interference after the match but Albion's Webster had little sympathy.
“It is a penalty," said Webster. "You get them given for less than that and we've had a few given against us so it was nice that it went our way for once.
"Pascal showed great character and nerve to stick it away.
“I felt that we created the better chances in the game. They had a couple of goals disallowed but in terms of clear chances we probably had the better of it and deserved something.”
The point moves Brighton to a respectable 10 points from their first 10 league matches and five points above the drop zone. Webster however believes Albion's displays have been consistent this season and more points will come.
“This season it feels that in a lot of games we haven't conceded many shots and Maty Ryan has not had a lot to do. Liverpool are the champions for a reason but we limited them pretty well on Saturday.
“We feel like we are building something. Each game throws up different challenges and it's not easy to pick up points in the Premier League but if we maintain the consistency of performances the results will come.”
Webster and Brighton now have eight days to recover and prepare for their next Premier League match which is against Southampton at the Amex Stadium on Monday, 7 December, kick-off 8pm.