The win was the Reds' seventh straight league triumph and saw them break a club record by earning a tenth successive clean sheet.
The Spanish striker's double act came as Liverpool's winning run looked to be coming to an end against Steve McClaren's stubborn side who had Chris Riggott sent off late on.
Liverpool welcomed back Xabi Alonso who sat out the midweek stalemate at Stamford Bridge. Morientes replaced Luis Garcia and there was also a rare start for Harry Kewell, although Didi Hamann missed out after failing to remove Michael Essien's studs from his shin in the last four days.
Seeking to avoid their fourth straight away defeat in the Premiership, and on the lookout for their first Anfield league win since 1976, Boro boss McClaren made two changes from the battling 1-0 reverse at Chelsea bringing back Mark Viduka and Emanuel Potagez.
Full of confidence, it was Liverpool who made all the early running with skipper Steven Gerrard finding space for three early long-range strikes, the latter a blistering strike from 30 yards which worried Mark Schwarzer.
Boro took early encouragement from Liverpool's carelessness in possession in the opening stages and there were signs that the Reds' miserly backline could be troubled.
Some neat interplay from the visitors around the Liverpool area suggested they could unlock the safe, but they failed to muster a shot in anger in the first half.
The first real chance came midway through the half when John Arne Riise's long throw bounced through to Morientes who forced Schwarzer into a smart save. From the resulting corner Peter Crouch had a header cleared off the line.
Liverpool were picking up. Mo Sissoko's influence in the centre kick-started a number of Reds attacks from which they would bombard the Boro penalty area with crosses. More often than not Crouch and Morientes would rise highest but neither could get a clean header away.
Five minutes before the break the rampaging Sissoko headed straight into Schwarzer's arms following a supreme knock-down by Crouch. An unbelievable last-ditch challenge from Riggott blocked Crouch's effort only two yards from goal before the sides went in at the break goalless.
A distinctly offside-looking Mark Viduka had a magnificent chance to break the deadlock on 47 minutes when, after sending Pepe Reina the wrong way, struck the ball against the Spanish keeper's legs. A foot higher and McClaren's side would have been celebrating an unlikely lead.
But Liverpool fired back. Riise blasted over with a beautifully struck left-footed volley, Crouch had a half-shout for a penalty, Morientes headed straight at Schwarzer, and Kewell forced the Boro keep to scramble back to tip over a fine lobbed half-volley - all in a ten-minute spell.
Just as it seemed the frustrated Reds may have to settle for a point, they had the lead through a richly-deserving Morientes. Luis Garcia, who was brilliant after replacing Crouch, floated over a cross that was smartly dummied by Gerrard, leaving the Spaniard in the clear to slide home his second League goal of the season.
Reina was forced into another fine save from Viduka, who presented Boro's only threat, before Morientes doubled his tally with a peach of a lob over Schwarzer from 20 yards - again thanks to a Garcia pass.
Riggott was dismissed five minutes from time for his second yellow card, a lunge on Gerrard, as McClaren's day disintegrated. But for Liverpool, inspired by some classy Spanish flair, gave further evidence of their credentials to mount a future challenge to Chelsea. They set off for Japan tomorrow and within a week could be crowned the World Club Champions.
MAN OF THE MATCH: Fernando Morientes (Liverpool) - Richly deserved to be on the end of the game's two best crosses. He finished with aplomb, worked hard and gave Liverpool an injection of class that they needed to overcome Boro.