The Reds, who rotated their squad at the interval to give 21 different outfield players a run out, netted twice either side of half time for a convincing victory.
There was a chance just 40 seconds in for Seyi Ojo to open his account, as he brought down a ball over the top and rounded the keeper, only to then slice his finish wide of goal.
Joel Matip squandered a big opening of his own soon after, blasting over the crossbar from five yards out when a Milner cross was flicked into his path at the back post.
The breakthrough goal arrived 34 minutes in as Davies committed to getting a loose ball with his leg, only to catch a lively Ojo and concede a penalty, which Milner just about tucked into the bottom corner of the net.
Grugic was able to add a second before the break, brilliantly sending the ball past Davies from close to 30 yards out with a fizzed shot to put the Reds well in command at the interval.
Visiting boss Jurgen Klopp used the break to completely change his 10 outfield players, but there was certainly no break in momentum as Chirivella added a third goal five minutes into the second half.
Debutant Dominic Solanke saw his shot saved and Spanish youngster Chirivella was there to tap home, putting Klopp's men comfortably on their way to an opening-game win in their pre-season campaign.
Another bright spark in Woodburn was then denied by Davies after getting on the end of Solanke's cutback, while Andy Mangan was thwarted by Loris Karius at the other end, though both teams struggled for any real rhythm for most of the remainder.
There was time for a fourth goal of the night 11 minutes from time, however, as Woodburn was tripped inside the box when latching on to a Ryan Kent through-ball, before picking himself up and sending replacement keeper Luke Pilling the wrong way.
Much like Matip early on, Lazar Markovic somehow missed the target from close range when picked out, and a late chance also came and went for Solanke when he was denied by Pilling.