Substitute Matthew Taylor rescued a replay for Portsmouth after Michael Owen looked to have put Liverpool into the last eight.
Owen got Liverpool off to a flying start, rounding off a slick move in the opening minute by slipping the ball past Shaka Hislop.
Hislop produced two great saves from Didi Hamann to keep his team alive.
With 15 minutes left, Taylor drove in the equaliser from 10 yards after Liverpool failed to deal with a cross.
Liverpool exploded out of the blocks through Owen's beautifully crafted goal.
Steven Gerrard intercepted Eyal Berkovic's wayward pass and drove forward, swapping passes at pace with Bruno Cheyrou before slipping the ball to Owen who clipped the ball over Shaka Hislop's dive.
Gerrard then arrowed in a free-kick which almost surprised Hislop, but Portsmouth certainly had their opportunities, although too often their final pass lacked conviction.
1 min: Owen fires Liverpool ahead
32 min: Hislop great save denies Hamann
69 min: Another Hislop save keeps Pompey hopes alive
75 min: Taylor equalises for Pompey
Ivica Mornar pulled the ball back from the by-line only for Berkovic to get in the way as Alexei Smertin shaped to shoot, and hesitation between Jerzy Dudek and Sami Hyypia almost allowed Yakubu to sneak on to Petri Pasanen's cross.
Berkovic then set up Quashie who blasted over from 20 yards and as Pompey continued to ask questions of the Liverpool defence, Mornar again failed to provide a killer pass from the dead-ball line.
Pompey, though, had to rely on Hislop to keep them in the game when he showed fine reactions to beat away Emile Heskey's thumping shot from 16 yards.
Liverpool should have doubled their lead in the opening minute of the second half when Gerrard and Owen combined to set up Heskey but from 10 yards out the England striker blasted wide.
Another slick passing move set up Didi Hamann whose powerful goal-bound shot struck the unwitting Quashie and cannoned over the bar.
Amdy Faye provided Liverpool with a reminder of how fragile their lead was with a shot that ballooned up off Hyypia and momentarily threatened to loop over Dudek.
Owen got Liverpool off to a great start
Liverpool were doing just enough to keep their noses in front but on 63 minutes Owen's neat flick sent Gerrard into the box and as he went down under Dejan Stefanovic's challenge referee Mark Halsey gave a corner.
Pompey almost paid the price for Berkovic's poor free-kick which was picked up Gerrard who surged forward before curling a shot inches wide.
Portsmouth had let-off when Pasanen clipped Gerrard inside the penalty area and the foul was ruled outside. The resulting free-kick was cleared to Jamie Carragher whose searing shot brought another top-class save from Hislop.
Liverpool paid the price for sitting on their lead on 76 minutes when Smertin whipped in a cross which Henchoz failed to deal with and the ball dropped to Taylor who drove the ball the home.
Both sides had chances to win it, with Yakubu denied by Dudek's sharp save, and Anthony Le Tallec stabbing Gerrard's cross wide from six yards.
Liverpool: Dudek, Finnan, Henchoz, Hyypia, Carragher,
Kewell (Le Tallec 84), Hamann, Gerrard, Cheyrou (Sinama Pongolle 82), Owen, Heskey.
Subs Not Used: Kirkland, Murphy, Biscan.
Booked: Sinama Pongolle.
Portsmouth: Hislop, Primus, Pasanen, De Zeeuw, Stefanovic,
Smertin, Faye, Berkovic (Taylor 70), Quashie, Yakubu,
Mornar (Olszar 56).
Subs Not Used: Wapenaar, Schemmel, Hughes.
Booked: Smertin, Pasanen.
Referee: M Halsey (Lancashire).