Gerrard put the controversy over his summer contract saga to one side as he slotted in after just eight minutes.
The midfielder forced his way through to lob in for a second as the Reds predictably dominated against TNS.
The Welsh champions defended stoutly but Gerrard completed his triple with a low 20-yard strike after 89 minutes.
An impeccable period of silence was observed for the victims of the London bombings before kick-off at Anfield.
When the first qualifying round, first leg began, Liverpool were quickly out of the blocks as they looked to overpower the Welsh champions.
TNS manager Ken McKenna was afraid of being embarrassed by his side's illustrious rivals and he played with one striker in a strategy aimed at containing Liverpool.
But the Reds did not take long to break through the TNS ranks and it was Gerrard who gave the home side the lead.
Riise fired in a low cross which Anthony Le Tallec flicked onto the far post and Fernando Morientes passed for Gerrard to slot in from 10 yards.
Liverpool were denied a second when a stretching Gerrard could not get enough power to guide the ball past keeper Gerard Doherty from close range and the TNS stopper quickly recovered to block a Morientes follow-up strike.
The Merseysiders did not have to wait long for the second, however, as Gerrard caught the Welsh side's defence sleeping and raced through before lobbing the on-rushing Doherty.
Riise powered a shot just wide, Anthony Le Tallec had a flying header saved and Steve Finnan forced Doherty into a smart save as Liverpool bossed the match.
A 25-yard Gerrard curler went onto the roof of the net with keeper Doherty rooted to the spot but Liverpool chances started to become more sparse.
A sliding Le Tallec agonisingly failed to get a touch on a Warnock cross to the far post while Morientes headed over with a free header.
TNS were putting in a brave effort as they only gave their rivals fleeting sights of goal.
Djibril Cisse came on to add more bite to the Reds attack and they eventually added to their lead when Gerrard scored his third with a late effort.
Milan Baros was an unused substitute which heightened speculation that he may be sold, especially if the club sign Southampton striker Peter Crouch.