One week after last weekend's 1-0 defeat at Southampton, Marcelo Bielsa's Whites were heading for a second defeat in succession and a fifth loss of the Premier League season as Wolves led 1-0 heading into second-half stoppage time.
The Molineux outfit led via Hwang Hee-Chan's strike in the tenth minute but United were roared on by a determined Elland Road crowd who saw Leeds gradually create more and more chances.
United's stadium then erupted deep in second half stoppage time as referee Robert Jones pointed to the penalty spot after Joe Gelhardt was brought down and Rodrigo stepped up to slam home a 94th-minute spot kick to send the home faithful wild.
The record signing then raced away to celebrate in front of his side's fans - poleaxing the corner flag with a flying kick - and the Spaniard has hailed the influence of United's supporters.
"Amazing," said Rodrigo, speaking to LUTV.
"I think we pushed inside the field and the crowd and the fans feel that and push us on.
"The support was really, really important to keep going, to maintain the faith in getting the win or drawing the match.
"They helped us a lot."
Assessing whether snatching a point felt like a victory, Rodrigo reasoned: "Yes. I think we deserved more.
"We played really well, I think we dominated the game from the beginning to the end.
"Unfortunately we conceded a goal almost from nothing.
"It's true that we deserved more but it's true also that a goal in the last minute with this atmosphere, we feel like we won the game."