After a sleepy start, Daniel Agger settled the early jitters permeating Anfield with a smart header from Philippe Coutinho's corner to open the scoring on 36 minutes.
But it was Suarez, not for the first time this season, who orchestrated everything to help steer his team past tricky opponents and provide some festive relief after two defeats at title rivals Manchester City and Chelsea.
The Uruguay international had already got the ball in the net, nodding in Coutinho's free-kick, only to be denied by an offside flag and his creativity continued to spark, setting up Raheem Sterling with a cute nodded through-ball.
And while Jordan Henderson and Coutinho wasted chances to double the lead with dragged shots from close range, Suarez was becoming increasingly agitated with the treatment by David Meyler and Alex Bruce, who were marshalling the striker like two heavy-handed bouncers.
With just the single goal at the interval, there was still reason to be cautious for the hosts, especially playing a team who smashed in six second-half goals against Fulham at the weekend.
Any hope of a revival was extinguished in brutal yet beautiful fashion four minutes into the second period.
You may have excused Suarez for coming out after the interval in body armour, but he responded to Hull's enforcers by first winning a free-kick outside the box and then curling the dead ball over the wall into the top corner to make it 20 league goals this season.
Apart from tame shots by Robert Koren and Yannick Sagbo at the start of this contest, the visitors offered little threat and in the closing stages, they had their keeper Alan McGregor to thank for restricting the damage as he smothered a shot from the impressive Coutinho.
It was a thoroughly deserved victory for Brendan Rodgers and his team who climb back into the top four with Everton failing to beat Stoke and they will also be buoyed with a second-half appearance of fit-again Steven Gerrard.