It seemed so unthinkable three months ago, but Tottenham's visit to Anfield on May 15 will have plenty riding on it if Liverpool continue to play like this.
The pursuit of fifth place has appeared fanciful at times but for Tottenham or Manchester City to forget Kenny Dalglish's side, who are playing like they believe anything is possible, would not be wise.
Spurs still have a game in hand but their lead over Liverpool has been trimmed to three points.
Birmingham's hard-earned reputation for stubbornness -- they had drawn their previous seven league games against Liverpool -- mattered for little as the visitors were torn apart as the Anfield side took their tally to 27 points in 14 league games under Dalglish.
Two up at the break through Maxi Rodriguez and Dirk Kuyt, Birmingham could not get near them. Rodriguez, who replaced the injured Andy Carroll, added two more goals after the break to complete his hat-trick before Joe Cole scored a fifth.
"We were deserved winners and I think we played some fantastic football during the game as well so we've had a good day and it's very enjoyable," said Dalglish. "I don't think Maxi's a direct replacement for Andy Carroll, but he's got more goals just in that one performance.
"Maxi's a very intelligent footballer and the way the boys have worked in training has been a real credit in the way they've adapted to it."
With John Flanagan again on the opposite flank, left-back Jack Robinson, 17, made his first senior start and the pair played with an ease that belied their youth.
At the same time a midfield of Lucas, Rodriguez, Raul Meireles and Jay Spearing, rotated and never stopped moving, with some of their first-half passing representing a decent imitation of Dalglish's last great teams.
They took the lead with just seven minutes gone when Spearing, who finished last season on loan at Leicester City, hit a thumping shot that Ben Foster spilt and Rodriguez pounced to prod into the net.
The advantage was doubled midway through the opening period, despite Foster making up for whatever blame could be thrown at him for the opening goal.
Pepe Reina's kick was flicked on by Meireles and Luis Suarez's effort was blocked by Foster, who also got in the way of Kuyt's effort before the Dutchman rolled the rebound past a defender on the line.
Foster played on despite suffering a back problem and a dead leg in a collision with Stephen Carr in the build-up to the second goal but by the time he limped off four minutes before the interval, the visiting fans had already resorted to gallows humour.
A third goal came when Martin Skrtel, who had earlier attempted to dribble through a crowd of defenders in the opposition box, sent Suarez clear down the right and rather than hit a percentage cross into the centre he lifted the ball to the unmarked Rodriguez at the far post and the Argentine fired past substitute Colin Doyle. Rodriguez latched on to another rebound from his own shot to complete his hat-trick and there was still time for Cole to squeeze a shot past Doyle's weak save at the near post.
Alex McLeish's Birmingham are now just four points above the relegation zone with a game against Wolves to come next week.
"You lose early goals against the top teams and you think the other team has got an extra man and you're a man short, and it looked as if Liverpool were able to play as they liked and we never got close to them," said McLeish.
"We will recover."
Sunday Indo Sport