Goals from Algerian defender Nadir Belhadj and French striker Frederic Piquionne condemned Rafael Benitez's flops to their seventh league defeat.
Mascherano was dismissed for a horror tackle on Portsmouth defender Tal Ben Haim on the stroke of half-time.
Portsmouth had taken just 11 points from their opening 17 games and remain besieged by financial problems.
The hosts had a lucky escape when Steven Gerrard's goalbound shot was inadvertently blocked by team-mate Fernando Torres before being cleared.
Torres came within inches of putting Liverpool in front on 20 minutes with a majestic 20-yard curler, which had Portsmouth goalkeeper Asmir Begovic beaten before nestling on the roof of the net.
Gerrard's low left-wing cross almost led to a goal but the onrushing Torres narrowly failed to make contact six yards out.
Jamie Carragher, making his 600th appearance for Liverpool, produced a heroic block to divert Hassan Yebda's powerful volley behind for a corner from point-blank range.
Carragher was powerless to stop Belhadj giving Portsmouth the lead 12 minutes before half-time.
Kevin-Prince Boateng's driven low shot was palmed away by Pepe Reina but Liverpool failed to clear the rebound and the ball broke kindly for Belhadj, who lashed an unstoppable right-foot shot into the roof of the net from an acute angle.
Daniel Agger should have drawn Liverpool level just six minutes later when Gerrard's free-kick presented him with a free header at the back post but the centre-back nodded wide when it looked easier to score.
Liverpool were reduced to ten men on the stroke of half-time when Mascherano was shown a straight red card for a reckless lunge on Ben Haim.
Begovic, replacing the injured David James, produced a miraculous 67th-minute save to keep Portsmouth in front.
Gerrard's 15-yard piledriver struck two Portsmouth players on its way to goal but Bosnian Begovic somehow managed to readjust his dive and claw the ball behind for a corner.
Piquionne sealed the points eight minutes from time, brilliantly flicking up Boateng's cross before firing past Reina at the near post.