Last week the tables were turned. It was the turn of Suarez, now at Barcelona, to watch agog as Iago Aspas propelled Celta Vigo to one of the early shocks of the new La Liga season as the Galicians humbled the Catalan team 4-1 at the Balaidos stadium.
While Suarez is still warmly remembered at Liverpool for the 31 league goals he scored during that 2013/2014 season, Aspas is best remembered for taking a corner that has gone down in football blooper folklore after he passed straight to a Chelsea player in a 2-0 defeat at Anfield that all but ended the Merseyside club's title hopes.
Aspas never quite fitted in during the year he spent at Liverpool, making just 15 appearances before being loaned to Sevilla at the end of the 2013-14 season. So he came home to Celta on Spain's north coast, the club where he made his reputation in the town where he is a folk hero.
The 28-year-old Aspas was leading the line for Celta against Barcelona. He scored two sublime goals in that humiliation of the Liga champions. Manuel Nolito also scored -- and Sergio Alvarez made a string of spectacular saves at the other end, denying the world's most feared front three: Lionel Messi, Neymar and Suarez.
It was no fluke. Celta remain unbeaten in this league campaign and fourth in the table, two points off the surprise table-toppers, Villarreal.
No lesser authority than the Barcelona coach Luis Enrique said after the game: "If I have to lose, let it be against a team that plays like Celta."
Aspas was at it again on Saturday, coming on as a second-half substitute at Eibar and rescuing a point in a 1-1 draw as he bagged his fourth goal of the season.
Together with Real Sociedad's Imanol Agirretxe, Aspas is the second top scorer in La Liga, just one goal behind teammate Nolito and Real Madrid's Karim Benzema and Cristiano Ronaldo.
Aspas told CNN that Celta had been a bit jaded at the weekend after their midweek heroics.
"Of course, it affected all of us; playing against Barcelona requires even more concentration and such an amazing match left us even more tired than usual," Aspas said on his return to Vigo.
But he is enjoying football again, especially playing with Nolito and Fabian Orellana in an attack that opposing defences are learning to fear. "Playing with players of such quality always makes it easier," Aspas says.
And if the Barca game is any indication, he seems to have recovered his ability to run at (and often past) back-pedalling defences -- as Gerard Pique will testify.
Aspas has Celta in his blood. He joined their youth academy at the age of eight and it was his goals -- 23 in 35 games -- that helped Celta win promotion to La Liga in 2012. On the final day of the following season he provided the assist that rescued them from relegation.
He's even on record as saying he would never have a girlfriend from La Coruna, Celta's fierce Galician rivals just along the Atlantic coast.
Under coach Eduardo Berizzo, who was Marcelo Bielsa's assistant when the Argentine coached Chile, Celta play with pace, breaking fast and harrying opponents mercilessly. They also play high up the pitch, denying space to more sophisticated teams like Barcelona.
As a forward, Aspas says Berizzo's style suits him well. "He likes to play attacking football, to keep possession and exercise a lot of control over your rival and the ball -- and that brings a lot of chances," Aspas told CNN.
It's a philosophy that is employed by Mauricio Pochettino -- another Bielsa disciple -- when he was at Southampton and now at Tottenham Hotspur as well as Pep Guardiola at Barcelona and Bayern Munich.
It's demanding of the players' fitness, especially in a small squad, and requires discipline -- but when it works it stifles the opposition. Barca know.
The irony is that it was Enrique who set this transformation in motion when he was manager at Celta in the 2013-14 season. He introduced a passing game, in which three former Barcelona players -- Rafinha, Fontàs and Nolito -- were the foundations.
Xose Ramon Castro of La Voz de Galicia
was one of many to enjoy watching Celta under Enrique. "It was a team that took control of games, held onto the ball and attacked with clear ideas while maintaining balance in defence," he said.
Argentine Berizzo, a former Celta player, said in an interview last year that he was "empapado" -- or soaked -- in Bielsa's philosophy. The two first met when Berizzo was just 14 and Bielsa was youth coach at the club Newell's Old Boys, where Lionel Messi played for the youth team.
Like Bielsa, Berizzo says: "I like to take control of the game. I don't want to be dominated."
Enrique was certainly aware of the Celta threat. A few days before the game, he described them as "one of the most entertaining teams in European football."
Aspas isn't the first foreign player to struggle in England and then flourish in Spain.
Mexican Carlos Vela never made the breakthrough at Arsenal but scored freely after moving to Real Sociedad. Roberto Soldado was Tottenham's most expensive signing when he moved to London from Valencia in 2013. He scored just 16 goals in 76 appearances.
This year, Soldado came back to Spain and Villarreal, scored twice in the first two games and is one reason why the team lead La Liga.
Nor is Aspas the first player bought by Liverpool manager Brendan Rodgers (for $11.6 million in 2013), to fade into obscurity and move on a season after arriving.
In particular the loan of 21-year old Serbian international Lazar Markovic to Turkish side Fenerbahce this season has caused some head-scratching among Liverpool fans.
"Arriving with a promising reputation as one of European football's finest young talents, Markovic was never truly given the opportunity to impress," writes Jack Lusby on the This Is Anfield website.
Even Mario Balotelli is playing better in Milan than he did for Liverpool, though given how the Italian's season at Anfield panned out that's probably not hard.
Aspas, who scored just once for Liverpool -- against Oldham in the FA Cup -- is philosophical about his time on Merseyside.
"Everything helps you learn and gather experience," he said diplomatically. "And all that experience has helped me become a better player."