The Welsh champions had produced an outstanding display of organisation and effort to frustrate Liverpool for long spells at Anfield.
It looked like Gerrard's two first-half goals were going to be the only advantage they would take to Wrexham for next Tuesday's second leg until the Anfield skipper rapped home his third in the final minutes to ease nerves.
With 15 minutes left Djibril Cisse came on for Darren Potter and looked like he had created the third for Morientes with a fierce cross, but the ball had gone fractionally behind before the Spaniard slammed the cross home.
Nicky Ward was replaced by Leah on 81 minutes, TNS by now winning applause from the Kop for their defiance.
Cisse's fine run set up Morientes again, Evans stopping the effort and seconds later Morientes hooked over from 10 yards.
But Liverpool were looking short of ideas and they did not have the pace to really expose TNS, who were doing the Welsh Premier League proud.
Even the Kop's chant of 'champions of Europe' was sounding a bit flat at this stage - that is until Gerrard completed his hat-trick a minute from time when he struck an angled 20-yarder wide of Doherty's dive and inside the far post following Riise's crossfield ball.
Now a three-goal margin will be enough to make next week's second leg a cruise and a game that Benitez will now be able to use for experimentation.