The European champions' now 14-game winning streak in the league seemed set to end as Raul Jimenez cancelled out Jordan Henderson's early opener.
Liverpool were even grateful to goalkeeper Alisson Becker for not falling behind in the second half.
However, like crucial victories against Leicester, Aston Villa and Crystal Palace earlier in the campaign, Liverpool left it late to snatch another vital three points in their quest to end a 30-year wait to win the title as Firmino smashed home six minutes from time.
"You just have to find a way to win and have someone who makes the perfect decision and that was Bobby again," said Klopp.