Liverpool, who have now played two games more than second-placed Manchester United, travelled to the South Coast well aware that three points would see them wrestle top spot back from the defending champions.
But the Reds' under-fire manager Rafa Benitez raised a few eyebrows with his team selection - dropping star striker Torres to the bench and naming a defensive back three of Jamie Carragher, Martin Skrtel and Daniel Agger.
The visitors, who were without injured captain Steven Gerrard, settled into the new strategy imposed by their boss and had the best chance of the first half as Fabio Aurelio went close with a free-kick.
Pompey improved after the interval and were rewarded when David Nugent slotted the home side in front from former Liverpool striker Peter Crouch's 62nd minute pass.
Liverpool, though, were back on level terms seven minutes later as Aurelio superbly smashed in a 20-yard indirect free-kick to ignite hopes of returning to Merseyside with three points.
Benitez introduced Torres as the former Valencia boss pushed for a winner, but seconds later Pompey were back in front as Hermann Hreidarsson headed past Jose Reina with 12 minutes remaining from a Nadir Belhadj set-play.
Tony Adams' side looked set to hang on for the win, but substitute Kuyt - who had replaced David N'Gog - took advantage of some poor Pompey defending to fire an equaliser past David James from a tight angle in the 85th minute.
And then in time added on at the end of the 90 minutes, Torres headed past James to send Liverpool back to top spot.