The Albion forward fired home in emphatic style deep in added time to secure a 2-2 draw.
He ripped up a national script of Spurs climbing out of the drop zone under Roberto De Zerbi and sparked celebrations among away fans.
Rutter has had a largely frustrating season and lost his place in the starting line-up ahead of the recent good run.
But Fabian Hurzeler’s substitutes made big contributions at Spurs and Rutter’s goal rewarded his hard work on the training pitch in recent weeks.
Head coach Hurzeler said: “I think that can lead him to the next step in his improvement, in his development.
“He had a tough time, he went through it. He understood now what it needs to come back.
“He understood what he needs to invest on the pitch and off the pitch to improve.
“We should never forget he is still a young player.
“A young player always has waves in his development so he was now in a down, now he steps up.
“You see it also in training, he reacts well and that is why you get the rewards on the pitch.
“I think that is very important for him that, if you work hard, if you show the right effort every day, then you will get the reward.
“Other players are also in a low but you fight out of this low by showing the right effort every day.
“That is what he has showed and therefore he is now on the right way up.”
Rutter will be in contention for a start when Chelsea visit the Amex on Tuesday.
Hurzeler will update on his squad when he faces the media at 9am on Monday.
Diego Gomez and Kaoru Mitoma both went off injured at Spurs while James Milner was again absent.
Gomez in particular looked in great pain as he was helped off with a knee injury.
Hurzeler told BBC Radio Sussex: “It didn’t look good but let’s see how the next days go.”
Lewis Dunk, who travelled with the squad to North London, is available after a two-game suspension.