The hosts hit their stride straight away, and the brilliance of Suarez was the key to a fine opener, as the forward nutmegged Jonas Olsson before firing home.
The Uruguayan grabbed a picturesque second when his header from Aly Cissokho's cross found the top corner, before another header completed the treble after the break, when Suarez nodded home a Steven Gerrard free-kick.
James Morrison's penalty then didn't dampen the mood around Anfield for too long, as Daniel Sturridge capped the victory with a simply superb chip over Boaz Myhill.
Here are six lessons learned from a thoroughly impressive Anfield afternoon:
Has Anfield seen many better striking performances?
Luis Suarez was simply superb here, acting a one-man tour de force who was making a mockery of any suggestions that his commitment to the Liverpool cause was going to wane due to his summer-long desire to move away.
The forward will be playing in the Champions League next season, that much is obvious.
It'll either be in the shirt of another European superpower or wearing the red of Liverpool, a team he looks determined to drag toward the top.
He'd never scored against West Brom before the game either.
Aly Cissokho was good at Newcastle last week, but he was excellent here.
The Frenchman performed well in the left wing-back role, with his standout contribution coming when he teed up Suarez's superb second.
On this evidence, the on-loan Valencia man is working hard to earn a permanent move to Anfield, a switch which looks as though it would be good for both parties.
It has been said of Liverpool teams before, but it seems particularly true of this vintage. If they score a goal early on, you're in trouble.
Whereas earlier on in the season that meant that the Reds would look to successfully protect their one goal lead, here it meant that they could swarm all over their opponents, turning in a display which ultimately could have seen them score even more goals.
Tougher tests lie ahead, but if the Reds were to score early against, say, Arsenal next week, then the Gunners would be wise to be wary.
Jack Wilshere and Pajtim Kasami thought that they were fighting it out for the goal of the month crown between them, but Daniel Sturridge has now muscled in.
A personal opinion is that Kasami still leads the race, but Sturridge's special moment here was a joy to behold, and it put a deserved gloss on a fine display.
The forward now has eight goals in nine Premier League games this season, as well as 21 in 27 overall for the Reds
They are simply staggering statistics, and they only look like they're getting more impressive.
"From the knees" or not, Jordan Henderson was running everywhere here and was terrifically impressive as Liverpool dominated midfield.
The West Brom pairing of Claudio Yacob and Youssouf Mulumbu were key in their impressive results against Manchester United and Arsenal, but they were simply overrun by Henderson, Gerrard and Lucas here.
Henderson was the most impressive, and whilst others might want to make fatuous claims that the youngster will be in chronic pain when he's older, others would rather just enjoy his fine performances right now.
There are an increasing number of them.
Next Saturday's game at the Emirates has the potential to be a cracker, as Arsenal and Liverpool meet with their good starts to the season on the line.
Liverpool gained superb momentum with this result, and, with the prospect of Philippe Coutinho returning from injury, they'll rightly head for an admittedly impressive Arsenal with confidence.
With Suarez still in their shirt and in this form, how could they not?