Finland were keen to banish the all-too fresh memories of Friday's dismal 1-0 defeat at home to Malta, in what was Pukki's last competitive appearance for the Eagle Owls, who ended their 2026 World Cup qualification campaign on a sour note.
Oliver Antman cut inside and forced the Andorra goalkeeper Xisco Pires into a save 17 minutes in, then a minute late Antman enabled the home fans to forget all about Malta when he opened the scoring.
Latching onto a deflected through ball from Kaan Kairinen, the winger got in behind the Andorran defence and guided the ball past the goalkeeper.
Antman was then the provider of the moment all of Tammelan Stadion was waiting for with 26 minutes on the clock as the snow in Tampere got heavier.
A perfectly-time run again allowed the Rangers man to break through the Andorran defensive line, but this time he squared to Pukki in the centre. The man of the hour stumbled and fell under pressure from Max Llovera, but still managed to force the ball to trickle into the bottom corner.
Pukki's final goal for Finland will go down as one of his scrappiest, but neither he nor the adoring fans minded one bit. He had a chance for a second soon after, but this time Pires was equal to the attempt from a tight angle.
The HJK striker was again denied a brace within four minutes of a restart amid a goalmouth scramble at a corner, as he failed to force the home before Robin Lod had a follow-up effort blocked on the line. Then, on the hour mark, a loose ball fell to Pukki 12 yards out, but he fired it straight at Pires.
Soon after, Andorra thought they had been unfairly denied a route back into the match when Eric Vales headed Joan Cervos' free-kick past Lukas Hradecky, but replays proved the assistant referee was correct to raise his flag for offside.
But with a quarter of the match to go, Pukki played a part in wrapping up the win with a true passing-of-the-baton moment. Amid a flowing Finnish move, he received the ball at the edge of the area and teed up substitute Niklas Pyyhtia to score just six minutes into his international debut.
That assist proved to be Pukki's final act in a Finnish shirt, as he was substituted four minutes later, earning a standing ovation from all four corners of the ground and the warmest of receptions from his teammates and coaching staff.
A pair of Topi Keskinen headers in the final 10 minutes were the closest Finland came to a fourth, until his added-time cutback caused havoc in the Andorran box, and Leo Walta arrived to smash in the final goal of the night and begin the "Pukki Party".
Jacob Friis' side have ended a run of consecutive losses, while Andorra end 2025 without picking up a victory.