Virtanen had an unorthodox route into the main draw of the men's singles - after winning his first two qualifiers, a back injury forced him to withdraw from his final qualifier against Grigor Dimitrov, only to be given a lucky loser place in the first round following the withdrawal of Marin Cilic.
And the Finn appeared to have made a full recovery in time to face Rublev, surviving break point in the first game, before forcing a break in the second en route to a 3-0 lead. However, the Russian broke back in game five, and another in game nine put him 5-4 up and serving for the set, only for Virtanen to respond and ultimately force a tiebreak.
A crucial loss from Rublev saw Virtanen go 6-3 up in the tiebreak, and though the seeded player fought back on serve, he couldn't stop the Finn winning it 7-5 and taking the first set, 7-6.
In the second set, the man ranked 109th in the world survived seven break points - the final three of which were also set points - to force another tiebreak. Having been hanging on, Virtanen stunned his opponent by winning seven unanswered points, winning the tiebreak 7-0 for another 7-6 set win.
But that only seemed to galvanise the 23rd seed, who finally made the most of the break point chances he was getting, winning the third set 6-0 in just 28 minutes, as Virtanen wasted break point opportunities of his own in the second game.
Virtanen managed to get on the board at the start of the fourth set, but Rublev was now a man in form, and breaks in the third and fifth games soon had him 5-1 up, going on to win the set 6-2 and in a blink of an eye, the match was level again.
But the 25-year-old Finn, who reached the second round at Wimbledon earlier this summer, held his own in the fifth set, saving three break points as neither player could force their way through, sending the match to a third tiebreak.
However, this time things fell apart for the Helsinki man, who lost two of his first three serves to fall 5-1 down, and though he then began to win points on Rublev's serve, he gave the Russian one back for each he took, and the former four-time quarter-finalist at Flushing Meadow took the tiebreak 10-5.
The Moscow man therefore took a 6-7, 6-7 6-0, 6-2, 7-6 victory in three hours 45 minutes, and will meet Spain's Daniel Merida in the second round.