The Whites, for a second time in five days, required a goal deep in added time at Elland Road to secure a last-gasp 2-2 draw with Brentford in the Premier League.
Marcelo Bielsa' s side caused more chaotic scenes on Sunday afternoon thanks to the returning Bamford, who was handed his first appearance since mid-September due to an ankle injury.
The 28-year-old forward reacted quickest to a flick on from a Raphinha corner to turn the ball home from his knee off the underside of the bar.
The strike came in the fifth minute of injury-time on his comeback in LS11 and helped move Leeds six points clear of the top flight drop zone.
United's No 9 was introduced from the bench with around 20 minutes to go after the Bees had turned the game on its head in the second half.
Brentford trailed following a Tyler Roberts opener on his 100th Whites match but goals from Shandon Baptiste and Sergi Canos put Thomas Frank's outfit ahead.
Leeds battled back and grabbed a stunning draw just seconds before time expired which caused more wild scenes in the home stands.
"I always felt when I came on the pitch I was going to get one chance," Bamford reflected at full-time, with a smile on his face.
"It didn't come for ages and ages but I still thought there was time. [Adam] Forshaw said to me that I was going to get one chance and it came.
"The message [from the bench] was just to just try and give a presence in the area and spin behind, don't drop too short and just try and do what you can.
"I just tried to stay in the box as much as I could and hope I put myself in the right position."
The striker's return was his first inclusion in a matchday squad for nine games.
Bamford made one appearance for the club's Under-23s squad to regain match sharpness before being thrust back into Bielsa's senior set-up.
"I felt rusty. It's always going to be like that for the first few games while you get back up to speed," Bamford continued.
"It was just nice to get back out there. It's been frustrating because I set my sights on coming back in each match for about six games.
"It's weird. Sometimes when you're out through injury you become a better player all of a sudden and everyone starts dressing you up as some mighty hero.
"There probably was a bit of pressure. I just tried to do what I usually do. If I hadn't scored people would've said I wasn't fit and ready.
"The goal was nice, especially because it rescued a point. We had a 10 minute spell in that second half where they got the goals. Things just turned. It was frustrating watching from the sideline.
"It was important we got a result because the table is so tight at the minute."