Williams, watched by his family in the stands, lost a tight first set before tying the game to second on the center court, the place of seven of his 23 individual Grand Slam titles.
It was a break in the third, but Tan showed his resilience by fighting to make an exciting final set in a tie that bites his nails.
When asked if it was the last Wimbledon match of his decorated career, Williams said it was a question he “can’t answer.”
“Who knows where he’ll show up?” she added.
Williams played his first competitive games for nearly a year at Eastbourne last week, partnering with Ons Jabeur in the doubles event. The pair reached the semifinals, but had to retire after Jabeur injured his knee.
On Tuesday, he made his long-awaited return to the singles, a year after retiring in his last first-round match at Wimbledon.
The momentum shifted between the two players throughout the three-hour, 11-minute encounter, first in favor of Tan when he overcame the first set, then toward Williams as he recovered the second.
It looked like Williams, 40, would prevail in the decisive set while serving for the win, but the memorable comeback was not.
Tan broke the 5-5 and, despite not being able to convert a match point to 6-5, he wasn’t wrong when he had a second chance at the tie break.
Ranked 115th in the world, Tan played his first game in the Wimbledon main draw and ninth in all Grand Slams.
“When I saw the draw I was very scared,” he said after the match. “It’s Serena Williams, she’s a legend. I said, ‘My God, how can I play?’ And if I can win one or two games, it’s very good for me. “
Under the lights of the center court, Tan did more than that comfortably: he triumphed against one of the best athletes the sport has ever seen.
“For my first Wimbledon, it’s wow. Just wow,” he added, struggling to find the words to capture his emotions.
It’s still unclear if this was Williams ’last outing at Wimbledon. When asked to summarize her legacy at the tournament, she was concise, though underestimated.
“I think I’m pretty solid on the turf,” he said. “Maybe not today, but pretty solid out there.”
Christmas, Swiatek moves forward
In Tuesday’s previous matches on the central court, there were victories for this year’s French Open champions Rafael Nadal and Iga Swiatek.
Nadal, who won twice at Wimbledon, survived a scare to beat Francisco Cerundolo 6-4 6-3 3-6 and 6-4 as he began his quest for a No. 23 Grand Slam title, while that Swiatek recorded its 36th consecutive victory by winning. Jana Fett 6-0 6-3.
Nadal, who missed last year’s tournament due to injury, received a warm welcome on the central court, where he was tested hard by Argentine Cerundolo.
The Spaniard was looking for a regular 2-0 victory and a break in the third set, but Cerundolo, with a free spin, struggled with a double break to take the set.
The match seemed to be heading towards a decisive one when the world number 41 broke in the fourth, only Nadal saved his best for the last and sealed the victory with a double break.
Swiatek, meanwhile, dominated the first set against Fett in their first match since the French Open, but had to overcome a tough period in the second when Fett was close to getting a double rest.
The head coach has recovered from the unstable start of the set and has played five games in a row, increasing his streak of wins to 36 games.