Suarez, who was sensational throughout the first half, set-up Fabio Borini and Steven Gerrard to put the result beyond doubt by the break; the skipper netting his 150th Liverpool goal in the process.
Glen Johnson completed the scoring with a volleyed third from outside the box with 20 minutes remaining as a much-improved side that featured Pepe Reina and Lucas in the starting line-up, completed the task with efficiency to run out as 4-0 aggregate winners over their Belarusian opponents.
Liverpool were in the ascendency from the outset; the return of Suarez from Olympic duties with Uruguay adding a dimension that was missing from their trip to Belarus.
The striker, who announced earlier in the day that he would sign a new deal with the Anfield side, was cheered every time he touched the ball, and seemed to use the affection given by the crowd to boost his performance.
Switching between the left and right flanks, he was simply impossible to deal with and fed off the excellent service provided by both Gerrard and Borini to go test Gomel goalkeeper Vladimir Bushma four times inside the first 40 minutes.
And yet it was Suarez who turned provider when the goals were to be had. First he picked up a low pass inside the opposition box, used his skill to skip past his marker and saw his deflected cross fall to the feet of Borini, who scored his first Liverpool goal by volleying the loose ball under Bushma.
Then, after some wonderful build-up play from Jonjo Shelvey and Johnson, he nicked past his man again, drew Bushma off his line and then calmly pulled the ball across the face of goal to leave Gerrard with a six-yard tap-in that the England captain simply couldn’t miss.
Gomel, and in particular their Russian striker Aleksandr Alumona, had looked a threat during the first leg of this third round qualifying encounter, but with Lucas and Shelvey proving excellent where Jordan Henderson and Jay Spearing had been lacklustre a week earlier, the visitors barely got a look-in.
A more concerted effort to close off Liverpool’s attacks in the second half did at least keep the scoreline bearable, but in truth, the home side were worth far more than their three goals; the last of which came when Johnson’s volleyed effort from outside the box took a slight deflection off the back of Sergei Matveychik.
Brendan Rodgers, who oversaw a win on his first game in charge at Anfield, will see his side face more difficult opponents in the coming weeks, but the signs were encouraging. And with Swansea midfielder Joe Allen present in the stands to watch the victory ahead of a potential £10million transfer, there is every reason for the new boss to be optimistic of the season ahead.