Back-to-back defeats to rivals Manchester City and Chelsea had somewhat burst the bubble of being top on Christmas Day but returning to their Anfield fortress offered the security they needed to complete a workmanlike 2-0 win over Hull.
Daniel Agger's first goal since April had given the Reds a first-half lead but Suarez's free-kick just after the interval made him the joint-fastest player in Premier League history to score 20 goals. Andy Cole reached 20 for the season at Newcastle on New Year's Day 1994, but Suarez's goals have come from just 15 appearances.
It was no great surprise as the 26-year-old had scored in every home match this season, seven in a row after returning from suspension, with 14 in his last six at Anfield.
The sight of captain Steven Gerrard coming off the bench midway through the second half less than a month after sustaining a hamstring injury was as welcome as the club's return to the Champions League qualification places after dropping out since Christmas.
But after losing those two games against City and Chelsea this was almost the ideal response, grinding out a victory against a lower-placed rival who only a month ago had beaten them at the KC Stadium.
It was, in fact, the perfect antidote to all that Christmas excess. Plain, almost ordinary in parts, but somehow still quite satisfying and reassuring.
After an impressive 2013 for Liverpool the first half of football in the new year was dismal by their standards, although there was a degree of familiarity about the way they failed to test an opposition goalkeeper despite creating a number of chances.
Hull, for their part, began relatively well and comfortably held their own for half an hour but once they went behind they became increasingly niggly as they tried to knock their hosts out of their stride.
After two defeats in which it is safe to say they felt they did not get the decisions from referees, Liverpool would have been hoping the new year brought a change of luck but Craig Pawson, in charge of a Reds match for the first time in his maiden season as a select group official, offered little protection when Hull turned up the physicality.
Suarez, as is often the case, was the most offended against with David Meyler following through in conceding a corner 40 yards out, much to the Uruguayan's annoyance.
Later in the half the already-booked Alex Bruce appeared to catch the striker in the stomach in the build-up to Jordan Henderson firing a good chance wide.
But had Liverpool not won they would have had only themselves to blame as they wasted two good chances to put the game beyond Hull in the first half.
Suarez had already had a goal disallowed when he headed in Philippe Coutinho's free-kick having started in an offside position when he sent Raheem Sterling racing through with a clever header.
The youngster opened his body as if to shoot across Allan McGregor but drove straight at the Tigers goalkeeper from a narrow angle.
At least Agger was not so wasteful in the 36th minute when he met Coutinho's corner with his head and beat McGregor - aided by Jordan Henderson's attempts to get a touch in the six-yard box.
Henderson then wasted a better chance to score just before the break when he criminally missed the target after being teed up by Iago Aspas with Suarez still on the floor thanks to Bruce's unpunished challenge.
Half-time at least gave Suarez time to recover and it was Anfield which was left breathless five minutes after the restart when the Uruguayan produced another stunner which, due to their frequency, are becoming almost humdrum now.
Fouled by James Chester, the resultant 25-yard free-kick was an open invitation to the striker and he whipped home a brilliant free-kick, beating McGregor at his near post.
He may be the top flight's leading scorer by some distance - now seven and counting with City's Sergio Aguero still injured - but Suarez proved he is still human by ballooning a free-kick into the Kop late on.
Fortunately for him there were no more heroics required as only Liverpool's third clean sheet in their last 18 games ensured there was no anxiety as they head into 2014 on the up again.