The result in Austria ensured that Antwerp will also advance from Group J.
Elsewhere, Braga, AC Milan, Lille, Villarreal, Dinamo Zagreb, Red Star Belgrade, Slavia Prague, Bayer Leverkusen, Rangers, Benfica, Granada and Eindhoven ensured their places in the last 32 with one round of group games still to play.
They join Leicester, Arsenal, Hoffenheim and Roma who had already qualified.
In Linz, the hosts dominated the first half but only scored once, through Peter Michorl. Spurs, who had not managed a shot on target, won a penalty for handball in added time. Gareth Bale converted for his 200th career goal.
Son Heung-min put Spurs ahead on the counter attack in the 56th minute.
With Linz still threatening, coach Jose Mourinho made a series of defensive substitutions.
Tottenham had three centre backs, three full backs and two defensive midfielders on the field by the 84th minute when Johannes Eggestein still found a huge hole and lashed in a shot that Joe Hart reached but could not keep out.
Three minutes later, Spurs regained the lead. One of the two attacking players, Steven Bergwijn was tripped to earn a penalty and the other, Dele Alli, swept it home.
Spurs could not keep the lead. Young Frenchman Mamoudou Karamoko smashed in an equaliser from outside the box in added time.
Mourinho complained about the attitude of some of his team.
"The fact that the Europa League group phase doesn't motivate some of the players, I knew it," he said.
"When I saw the warm-up before the game I had a feeling and I told the players before the game that there was a huge difference in intensity, communication and enthusiasm in their warm-up and our warm-up because I was looking at both."
The draw was enough to put Tottenham through and next week they will host Antwerp, who beat Ludogorets 3-1, with first place at stake.
In Group H, AC Milan fell two goals behind at home to eliminated Celtic but rallied to win 4-2 and advance.
Tom Rogic and Odsonne Edouard scored for the visitors in the first 14 minutes, but Hakan Calhanoglu and Samuel Castillejo responded with two quick goals midway through the half.
'Catch your breath'
Jens Petter Hauger and Brahim Diaz, with a clever chip, struck in the second half.
"The lads wanted to test me, to see if I'd recovered," said Pioli, back on the bench after a bout of coronavirus.
"I'm happy for the reaction and the comeback, but also for qualifying with one round to spare."
"In this unprecedented time with so many matches close together, it's good to be able to catch your breath."
Milan are second in the group, one point behind Lille who also came from behind to win at home. Burak Yilmaz came off the bench in the 77th minute with. Lille losing to 10-man The Turkey striker poked home the equaliser three minutes later and smashed in the winner four minutes after that.
Celtic's neighbours city Rangers, advanced with 3-2 home victory over Standard Liege. The Belgians, who need to win, took the lead twice in the first half, but James Tavernier hit a penalty just before half time. Scott Arfield won the game in the 65th minute, running onto a pull back to end a crisp move with a precise low drive.
"We showed tonight what a team we are," said Arfield.
The tightest group is F where Alkmaar fought back to draw 1-1 with Napoli and La Liga leaders Real Sociedad came from behind twice to draw at home with Rijeka, who picked up their first point. The Italians lead by two points from Sociedad and Alkmaar and host the Basques next week.