Liverpool pummel sorry Pompey
Striker Fernando Torres scored twice and Italian Alberto Aquilani, starting for just the fifth time since joining for 20 million pounds from Roma, claimed his first goal for the Anfield club.
Dutchman Ryan Babel was also on target as Liverpool climbed above Manchester City into fifth place with 51 points from 30 games, one point behind Tottenham Hotspur who have a game in hand.
City have 50 points from 28 games and Aston Villa, also in the hunt for the final Champions League berth, have 46 points from 27 games.
Portsmouth, who look doomed to relegation after going into administration last month, grabbed a small consolation near the end with a well-worked goal from Nadir Belhadj.
With nine league defeats this season compared to two during the whole of the last campaign, Liverpool need a storming final couple of months to stand a chance of qualifying for the Champions League.
Rafael Benitez shook up his side after defeats by Wigan Athletic and Lille last week with Aquilani given a rare start in place of Lucas and Maxi Rodriguez in for Dirk Kuyt.
Portsmouth keeper David James was ruled out with injury before kickoff and the England international was replaced by youngster Jamie Ashdown who suffered a torrid six-minute spell midway through the first half.
Torres opened the scoring after 26 minutes when Ashdown's clearance was blocked and the lead was doubled two minutes later when Babel tapped in after good work by Torres. Aquilani then finished off a fine move involving Torres and Steven Gerrard.
Liverpool continued to carve out chances in the second half but had to wait until the 77th minute for Torres to score again before being substituted.
"The week has started well and hopefully that can continue," Benitez told the BBC.
Liverpool host Lille on Thursday trying to overturn a 1-0 deficit in the Europa League before going to Premier League leaders Manchester United on Sunday.