The two Spaniards' strikes were Liverpool's first away from home in the league since their last Premiership win on the road on February 1.
But their attempt to climb back into the fourth Champions League position was thwarted by news of a Duncan Ferguson winner for Mersey rivals
Everton against nine-man Manchester United.
Liverpool boss Rafael Benitez, who kept Steven Gerrard on the bench for 68 minutes, will be delighted, however, with his side's sharp display against a Pompey side always difficult to beat at Fratton Park.
The home side certainly showed their fighting qualities as record signing Diomansy Kamara smuggled in a 33rd-minute equaliser but it took a bold display by keeper Jamie Ashdown to prevent Liverpool winning convincingly.
There were near misses and spurned opportunities aplenty in a thrilling first half and there was more of the same after the break.
The £6 million Morientes netted at the second attempt from John Arne Riise's cross in only the fourth minute but Lomana LuaLua had already had an effort disallowed and Milan Baros wasted a good chance.
And Morientes should have scored a second goal for Liverpool in the 26th minute when after a raid by Sami Hyypia, Steve Finnan's cross found the tall striker unchallenged 10 yards out at the far post, but he headed off target.
Pompey were guilty of poor marksmanship, too. Kamara hesitated inside the Liverpool area when a chance looked like opening up and when a lovely ball by Gary O'Neil sent LuaLua in to lob neatly over Jerzy Dudek, the keeper scrambled back to palm away under the bar.
Pompey raised the volume with an equaliser two minutes later by Kamara following an O'Neil corner.
Dejan Stefanovic flicked on, Arjan de Zeeuw's diving header came back off a post and Kamara forced home the rebound for his sixth of the season.
But Kamara spurned another opening to put Pompey ahead eight minutes later when a piece of magic by LuaLua left him one-on-one with Dudek only for the keeper to spread himself bravely and block the shot.
And although they were lucky not to pay for that when Riise shot wide from a Xabi Alonso cross on 42 minutes, there was no stopping Luis
Garcia heading the visitors back into the lead from a Riise cross in first-half injury-time.
Pompey were indebted to keeper Ashdown for preventing Liverpool wrapping up victory early in the second half when he stuck out a foot to stop Riise's drive, held Baros' shot on the turn and tipped over a Riise rocket before defying the same pair with a brave double save.
Yet Steve Stone should have put the home side back on level terms on the hour when he overran the ball inside the six-yard box following Matthew Taylor's cross and ended up losing it altogether.
It still seemed only a matter of time until the Pompey goal was pierced again but when they brought on ex-Liverpool man Patrik Berger who scored the winner against them last year they had more firepower and Dudek had to make a flying save to keep out the midfielder's 25-yarder.
Ashdown's outstanding stop to defy Xabi Alonso right at the end was typical of the contest.
PORTSMOUTH: Ashdown, Cisse, Stefanovic, De Zeeuw, Taylor, Stone, Skopelitis, Hughes, O'Neil, Kamara, LuaLua.
LIVERPOOL: Dudek, Finnan, Hyypia, Carragher, Traore, Luis Garcia, Alonso, Biscan, Riise, Baros, Morientes.
Referee: H Webb (S Yorkshire)