The Uruguayan was again the match-winner for the Reds as his two goals helped Dalglish's men come from a goal down, after Kenwyne Jones had given Pulis' men the lead.
Luis Suarez’s brilliance proved to be the difference between the two sides as Liverpool came from a goal down against Stoke to run out 2-1 winners at the Brittania Stadium on Wednesday.
Suarez scored twice for the Reds after Kenwyne Jones' opener right before halftime.
The visitors began the brighter of the two sides, with Dalglish’s men looking to take advantage of the height of Andy Carroll and the pace of Suarez.
Liverpool looked threatening on the break, and following hesitant play from Glen Whelan it broke well and found itself four on two, only for Jordan Henderson’s cross to be well intercepted by Robert Huth.
The away side really should have taken the lead through Suarez. Maxi Rodriguez’s cut back found Suarez, who did well to stay onside, but his 12-yard effort was parried by Thomas Sorensen.
Against the run of the play the home side thought it had taken the lead shortly after the half-hour mark.
Following a typical Rory Delap throw-in, Jonathan Walters nicked in ahead of Pepe Reina to head home. Similarly to Grant Holt’s equaliser at the weekend, Reina was left all at sea, only this time his blushes were spared by referee Lee Probert, who deemed Walter’s to have fouled Reina to the bemusement of the home crowd.
Shortly after, the home side did take the lead. Uruguayan defender Sebastian Coates was hassled by Jonathan Walters, who, after nicking possession, drove to the byline before cutting back to find Jones, who stooped to head home and give his side a surprising halftime lead.
It didn’t take long for Liverpool to restore parity. Just a few minutes after the break, Suarez received the ball on the corner of the 18-yard box, and after nutmegging Stoke fullback Ryan Shotton he curled a superb effort into the left-hand side of Sorensen’s goal, leaving the Danish goalkeeper helpless.
Tony Pulis looked to shuffle his pack shortly after the equalizer, as the away team began to take control of the game. Cameron Jerome was brought on to replace Matthew Etherington and Jermain Pennant replaced Ryan Shotton.
Similarly, Kenny Dalglish started to ring the changes, with Craig Bellamy replacing the ineffective Maxi Rodriguez, as both managers appeared to be readying themselves for extra-time.
Bellamy almost had an instant impact, striking the post from the edge of the 18-yard box after good hold up play from Andy Carroll.
Just minutes later it was the Suarez show once again. The little Uruguayan latched on to a lobbed ball from Henderson at the back post to give his side the lead just minutes from time.
Suarez limped off just seconds after celebrating, to a rapturous standing ovation from the 4,000 traveling Liverpool fans, as his two goals proved enough to send Liverpool into the quarterfinals.