Minamino opened the scoring early in the first half as he continued his impressive pre-season form.
Firmino, fresh from his extended break, lit up Anfield as he bagged a brace. The Brazilian looked back to his best after a disappointing campaign last season, subsequently giving Jurgen Klopp a selection headache just days before Liverpool's season opener against Norwich.
The story of the match
It was a slow start to proceedings at Anfield and that was unsurprising given that Klopp had selected a entirely different side to the one that featured in Sunday’s friendly - predominantly featuring those who were in the earlier stages of their pre-season preparations.
Minamino gave the 40,000 fans packed inside Anfield a clear indication that he was chomping at the bit to impress, after a difficult first 18 months in English football.
He had the games first chance with just 13 minutes gone on the clock, Liverpool new boy Ibrahima Konate had Reds fans purring early into his first Anfield start after his clipped ball landed perfectly into the stride of the Minamino. But he was unable to out fox Ossasuna goalkeeper Juan Perez, as he somehow managed to tip it just inches wide of the far post.
However, Liverpool's No.18 showed no signs of letting his earlier miss dent his confidence as he made amends minutes later by firing the Reds into the lead.
Fabinho was the provider this time, outlining why he is so important to Klopp's side, as he split the La Liga sides defence with a perfectly weighted ball into the path of the Japanese international. Who, this time, made no mistake with the finish as his effort looped over the head of Perez thanks to a deflection from an Osasuna man.
The heart-felt roar that followed Monday night’s opener was deafening. This was certainly no ‘friendly’ for those inside Anfield - with most making returning to their place of worship after a 15-month hiatus .
Moments prior to kick-off, Liverpool's stalwart left-back Andy Robertson announced that he had suffered ligament damage in Sunday's draw with Bilbao - ruling him out of the Reds' opening Premier League fixtures.
Kostas Tsimikas soon helped Liverpool double their lead as he did his best to ease any fears fans have about the imminent absence of the Scotsman.
His low-driven cross, which followed some wonderful, intricate combination play with Minamino, gave Firmino the simplest job inside Anfield as he converted home from close range.
Klopp’s men were cruising, two goals to the good after 20 minutes, and didn’t the Kop know it.
The only dampener on the night would occur on the half-hour mark as Curtis Jones was forced off after he was bundled over into the Osasuna technical area and received a blow to the head. In a move to combat any potential concussion, the midfielder was replaced by Ben Woodburn.
The game was wrapped up moments before half-time as the Reds capped off an impressive first half performance with a breathtaking counter-attack.
Firmino and Woodburn linked up perfectly on the edge of their own half before the 21-year-old’s clipped pass found the on-running Minamino down the left flank.
The former RB Salzburg man picked out Firmino, who set himself with a stylish piece of chest control before slotting past Perez to grab his second and Liverpool’s third.
Like any friendly, the second-half was played at a more pedestrian-like pace. But Alex Oxlade-Chamberlain continued to conduct the show on the Anfield stage as his confidence was epitomised by a robonna cross.
The La Liga side continued to offer Liverpool the time and space to distribute the ball to either flank as the Reds displayed their prowess from crosses - with Divock Origi heading Neco Williams' whipped cross just over.
Perez became the Kop's newest enemy when he denied Firmino from taking home the match ball as he smothered the Brazilian's close range header.
With 20 minutes remaining, Osasuna made sure they had a goal for their efforts. Kike Garcia headed past Caoimhin Kelleher from close range following a delightful ball from Ruben Garica.
There was a flurry of late chances in front of the Kop for the likes of Rhys Williams, Origi and Oxlade-Chamberlain but none of the trio were able to grab the much-craved goal to round the contest off.
Liverpool may not have grabbed a fourth goal but the Kop welcomed back, their captain, Jordan Henderson as he made his first club appearance since his February - yielding arguably the loudest cheer of the evening.