The 26-year-old summer signing from Celta Vigo has endured a difficult start to his Anfield career and never looked comfortable in the Premier League.
Wearing the number nine shirt for Liverpool carries significant history and expectation considering the greats who have graced it in the past.
But Aspas was handed the responsibility of leading the line with 20-goal striker Luis Suarez rested and he eventually delivered with a decent strike 10 minutes after half-time.
James Tarkowski’s late own goal, diverting in Raheem Sterling’s shot, gave Liverpool the cushion they needed – especially as they were down to 10 men after Daniel Agger was forced off injured with three substitutions already made.
There was to be no fairytale repeat of Oldham’s fourth-round victory over the Reds last January and Liverpool can now look forward to a trip to either Bournemouth or Burton Albion.
The accusation levelled at Liverpool is they are a one-man team – and that man was on the bench as the Reds toiled with little impact in a first half which did even less to warm the majority of the 44,102 crowd inside an icy Anfield.
Assistant manager Colin Pascoe, at Friday’s pre-match press conference, suggested Suarez would have kicked either him or manager Brendan Rodgers had they suggested dropping him.
But rest him they did and the only kicking the Uruguay international did for 76 minutes was his heels on the bench.
What he saw, the first half in particular, would have frustrated him as much as everyone else.
With six changes from the New Year’s Day win over Hull it was perhaps not surprising it took a while for the home side to develop any sort of control or rhythm.
Fringe players Aspas and Luis Alberto, both summer signings, were given rare starts but both failed to take their opportunity against a side 19th in League One.
Only three of the starting XI – goalkeeper Brad Jones, Jordan Henderson and Raheem Sterling – experienced the 3-2 humbling at Boundary Park just over a year ago.
While Oldham were the aggressors on that day they arrived at Anfield with a slightly less positive game plan, initially looking to contain.
That plan worked longer that they probably hoped for as Liverpool looked toothless for 45 minutes.
Alberto had a promising half, drifting one shot wide from Victor Moses’ lay-off and having another batted away by goalkeeper Mark Oxley.
Sterling was less effective, which was all the more infuriating for Liverpool considering the majority of their limited opportunities fell to him.
Steven Gerrard’s position as a deep-lying midfielder denied the home side an attacking thrust going forward despite Henderson’s best efforts and so the introduction of Lucas Leiva for Alberto at half-time provided a welcome release for the captain.
Immediately Liverpool seemed to find another gear, also helped by the introduction of Philippe Coutinho for the ineffective Moses, and within 10 minutes they had broken the deadlock.
Sterling finally found an end product worthy of the name and Aspas produced a finish Suarez would have been proud of, hooking home the cross right-footed.
If ever a player needed a boost it was the Spaniard, whose start to his Liverpool career has been disappointing to say the least with a lengthy lay-off with a thigh injury not helping.
It was as though a weight had been lifted off his shoulders and it was something of a surprise to see the previously lightweight forward jump highest in the penalty area to head Sterling’s next cross against the post.