The Brazil international curled an 87th-minute long-range shot past goalkeeper David Raya on Sunday to decide a thrilling game that's now cut Arsenal's lead to just four points, ahead of Manchester City and Aston Villa.
"These are the kind of games we dream to play in," Cunha beamed afterwards. "The games that we watch on television and we want to be part of."
United are up to fourth after back-to-back wins under coach Michael Carrick, who has started brilliantly in making his case to be given the job long-term, having beaten Man City in his previous game.
So, two games in, Carrick has defeated the top two teams in England - but for Arsenal, it's three games without a win in the league to give hope to their title rivals. This was their first home loss this season, despite taking the lead in the 29th through Lisandro Martinez's own-goal.
"He's been brilliant with us. He's brought a fresh energy and the group has really galvanised," said United defender Harry Maguire of former England international Carrick.
"Two tough games and everyone probably thinks we are going to come away with not many points. But to win both is magnificent."
If that was a gift, so was United's equaliser, with Martin Zubimendi's loose pass playing Bryan Mbeumo through on goal. The Cameroon forward rounded Raya and fired into the empty net in the 37th.
Patrick Dorgu then crashed in a spectacular long-ranger that went in off the underside of the bar five minutes into the second half to put United in front.
But Mikel Merino bundled in an equaliser in the 84th that looked to have at least salvaged a draw for the home team -- until Cunha's outrageous winner.
Villa kept up their unlikely title challenge with a 2-0 win at Newcastle with a goal in each half from Emiliano Buendia and Ollie Watkins.
Buendia fired Villa ahead with a dipping shot from outside of the area in the 19th minute and Watkins doubled the lead in the 88th.
Villa haven't won the title since 1981 and seven years ago were playing in the second-tier Championship, but under coach Unai Emery, the Birmingham club have been transformed.
This was their 13th win in their last 16 league games.
Chelsea are also going in the right direction under new coach Liam Rosenior, with goals from Estevao, Joao Pedro and Enzo Fernandez sealing a 3-1 win at Crystal Palace.
Rosenior has now begun by winning four of his five games in charge in all competitions, with two coming in the league.
At the bottom of the standings, Nottingham Forest picked up a crucial 2-0 win at Brentford to reopen a five-point gap to the relegation zone.
West Ham's 3-1 win against Sunderland on Saturday had enabled the London club to move to within two points of 17th-place Forest, but Igor Jesus and Taiwo Awoniyi got the goals in each half that allowed Sean Dyche's team to stretch clear.
