Andrey Rublev edges into Australian Open second round after five-set thriller
"For sure I will not forget this match," he said. "Thiago is a super-dangerous player, super-talented when in the mood."
The fifth seed suffered the indignity of being broken in his first service game but recovered from a 0-3 deficit to take the first set.
The Russian, who warmed up for the first Grand Slam of the year by winning the Hong Kong Open, was quickly into his stride in the second set, racing into a 5-1 lead and threatening to sweep his opponent aside.
He was pegged back by 78th-ranked Seyboth Wild but regained the initiative, putting away a volley at the net to move into a two-sets-to-love lead.
It looked only a matter of time before Rublev wrapped up the win but Seyboth Wild was not finished and a single break in the third set kept him in the fight.
The 23-year-old Brazilian, who upset Daniil Medvedev at Roland Garros last year, broke in the seventh game of the fourth set and levelled at 2-2 on a rapt Margaret Court Arena.
A nerve-jangling deciding set went with serve, with Rublev moving 6-5 ahead.
In the next game Seyboth fell to 0-40 under intense pressure from the Russian but he fended off those match points plus another to take the match to a tie-break.
The Brazilian raced into a 4-1 lead and then led 6-4 but Rublev stayed in the fight deep, winning the last six points and sealing the match with an ace.
He collapsed to the ground before letting out a guttural roar.
Rublev admitted that he relaxed in the deciding tie-break, believing he was heading out of the tournament.
"When I was losing 4-1, mentally I gave up and maybe that's what helped me in the end. I felt it's not my day but then I hit some good serves and good returns."