Harrison produced his first goal in senior English football to buck Leeds’ bad record at the New Den and force a 1-1 draw with a minute of normal time to play.
The on-loan Manchester City winger struck from 20 yards, averting a first league defeat of the season and the first of Marcelo Bielsa’s reign as head coach.
Harrison described the result as “crucial” on a day when potential promotion rivals Middlesbrough and Derby County both lost but admitted an injury-affected Leeds side showed room for improvement during a tough scrap in Bermondsey.
Leeds, who had lost eight of their previous nine visits to Millwall, fell behind to 55th-minute strike from Jed Wallace and were on the verge of defeat when Harrison struck.
“It was definitely a big result after realising that Middlesbrough had lost and that Derby had lost as well,” he said. “If we want to get promoted then this is going to be an important time to get points. It’s crucial and we’re happy to get a point but in the end we’ll be looking to play better.
“It shows we have a lot of character in the team. As soon as they scored it was almost like a switch went off and the team started to play the way we have been playing throughout the season. We used that to our advantage.
“It’s important to not lose sight of what we ultimately want but we have to take it game by game. It’s important not to get distracted but I think we’re definitely a team capable of getting promoted.
“We just have to keep our heads straight and keep on the same path.”
Injury deprived Bielsa of Pablo Hernandez, Kemar Roofe, Gaetano Berardi and Patrick Bamford in the lead up to yesterday’s game and a shortage of strikers left Harrison playing as a centre-forward for the final 22 minutes after Bielsa withdrew league debutant Tyler Roberts.
Harrison, who joined Manchester City from New York City in January and came to Leeds on a season-long loan in July, found a way through when a loose ball dropped to him on the edge of Millwall’s box.
Leeds then survived an onslaught in injury-time as Tom Elliott hit a post and Tom Bradshaw and Conor McLaughlin both came close to snatching a winner.
Harrison said: “It was a very special moment and a crucial time. With the momentum they had it was a good time to get the goal and once I did score it I was hoping to get another one.
“I tried to use the momentum to get another but the last five minutes were really tough, playing in a tough stadium against a tough side. It was really challenging but I’m happy to get my first goal.”
United host second-from-bottom Preston North End at Elland Road on Tuesday in the second of three matches in eight days. Hernandez, Roofe, Berardi and Bamford are all expected to be absent again.