The Reds won 3-1 on the night, but the scoreline wasn't enough to go through at the expense of Russian outfit Zenit Saint Petersburg, who prevailed 3-3 on aggregate courtesy of Hulk's away strike.
The goal of the first leg had been scored by the same man, and the Brazilian was on hand to latch onto Jamie Carragher's horrifying mistake and slot coolly past Pepe Reina inside the opening 20 minutes.
But Anfield just got noisier.
Suarez scored his first free kick just left-of-centre, but the Zenit wall played a big role. It parted like the Red Sea to allow the Uruguayan's strike—which would have been blocked on any other night—to slither through and find the near corner of the net.
After Joe Allen poked home a second, halftime in Merseyside was abuzz with optimistic noise: Could Steven Gerrard and Co. really pull off such a momentous win?
The second half started in a similar fashion—Liverpool working the flanks well and applying huge amounts of pressure to Zenit's back line. Stewart Downing and Jose Enrique were looking particularly ominous, but it was that man Suarez who won a free kick 25 yards from goal.
As the Kop end chanted for captain Gerrard to have a go, Suarez ignored the clamours and fired in what can only be described as a beauty.
With the ball placed dead centre of goal, the former Ajax forward was able to go either way, and Zenit goalkeeper Vyacheslav Malafeev failed to claw the ball away as it sailed inside his left-hand post.
What a strike!