The Swans claimed a hard-fought and deserved point as they came from behind to hold Manchester United at the Liberty.
Patrice Evra had headed the visitors ahead in the 15th minute but Michu tapped home to level on the half-hour mark for his 13th Barclays Premier League goal to make him the top-flight's top scorer.
Both sides went close to a winner, Robin van Versie struck the woodwork while Michael Carrick saw his header touched onto the crossbar by the returning Michel Vorm.
Ashley Williams, man of the match against Tottenham Hotspur the previous week, made a number of blocks in the heart of defence but Wayne Routledge and Kemy Agustien also threatened at the other end.
But in the end, the Swans were happy to add another point to their tally - now 24 - as they remain 11th and nine points clear of third-bottom Wigan going into the post-Christmas Day fixtures with Reading and Fulham.
The Swans made two changes to the starting XI that lost at Tottenham Hotspur last time out.
Michel Vorm returned from the groin injury sustained in the defeat to Manchester City in October, which meant Gerhard Tremmel dropped to the bench.
In midfield, Kemy Agustien made his first league start of the season as Ki Sung-Yueng dropped to the bench ahead of a busy festive schedule.
Angel Rangel was still missing, which meant Dwight Tiendalli continued at right-back while Pablo Hernandez remained injured.
Manchester United were without Rio Ferdinand and Nani, though Nemanja Vidic led the side as he made his first start since September.
Swans: Michel Vorm, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton (Ki Sung-Yueng, 61), Kemy Agustien (Itay Shechter, 87), Jonathan de Guzman (Luke Moore, 70), Nathan Dyer, Wayne Routledge, Michu.
Subs: Gerhard Tremmel, Jazz Richards, Garry Monk, Danny Graham.
Manchester United: David de Gea, Patrice Evra, Phil Jones, Jonny Evans, Antonio Valencia (Javier Hernandez, 61), Wayne Rooney(Ryan Giggs, 78), Nemanja Vidic (capt), Michael Carrick, Ashley Young, Robin van Persie, Tom Cleverley (Paul Scholes, 86).
Subs: Anders Lindegaard, Danny Welbeck, Darren Fletcher, Alexander Buttner.
With a superb atmosphere at the Liberty, the Swans pressed first with Ashley Williams's fine cross-field pass finding the on-rushing Michu, but the Spaniard couldn't keep his first-time effort down.
Wayne Routledge then fired straight at David de Gea following a fine run by Jonathan de Guzman as the Swans made a bright start in the opening ten minutes.
Michu then probed again, racing on to Routledge's through ball, but his effort was easily dealt with by de Gea.
Then Manchester United replied via Wayne Rooney, and Michel Vorm did well to swat his deflected shot away, before the keeper was called upon again to push Ashley Young's low drive wide for a corner.
But from the set-piece, the visitors got themselves ahead with 15 minutes on the clock. Patrice Evra rose highest and his header crept inside the post.
The Swans needed a response, and they went close to an equaliser as de Guzman latched onto a loose ball and raced on, but referee Michael Oliver adjudged Jonny Evans' path.
Michu headed over a Nathan Dyer cross before the Swans deservedly got themselves on level terms.
On the half hour mark, Routledge's superb pass found de Guzman, whose close-range shot was parried by de Gea straight to Michu, and the Spaniard tapped home his 13th Premier League goal.
The Swans pushed again, de Guzman beating Tom Cleverley to the ball as the midfielder attempted to shield it out for a goalkick, but the Dutchman won possession and ran towards goal but his shot was straight at de Gea.
The de Guzman flashed an shot along the face of goal before Dyer's low drive was collected by the Spanish stopper.
But then Vorm was called into action as he had to collect his initial save after Evra found Wayne Rooney from 12 yards out in the last action of the half.
Half-time: Swans 1 Man Utd 1
The second half promised as much action as the first, with Kemy Agustien's low left-footed shot collected by de Gea before Williams and then Chico Flores denied Rooney.
Routledge went even closer as he collected Dyer's pass inside the box before blasting an effort which de Gea palmed out for a corner.
The end-to-end action continued, Williams diving in to block Young's shot from an acute angle.
Both managers then made changes, with Ki Sung-Yueng replacing Leon Britton while United boss Sir Alex Ferguson swapped Javier Hernandez for Antonio Valencia on the 61st minute.
United then went within inches of taking the lead, Phil Jones' cross being flicked on by van Persie, but the Dutch striker's effort beat Vorm but not the crossbar.
Luke Moore then came on in place of de Guzman, who was given a standing ovation by the Jack Army, for the last 20 minutes.
It saw Moore move up front with Michu dropping into the attacking midfield role as both sides looked for a winner.
Rooney went close with a free-kick before he was replaced by Ryan Giggs, and moments later United went within inches of taking the lead.
Michael Carrick's thunderous header from a corner looked goalbound, but Vorm got a hand on it to deflect it onto the crossbar.
United came again moments later, Giggs threading a pass through to Evra, whose cross found van Persie, whose shot was blocked by Williams before Young tried his luck with the loose but Ben Davies blocked.
Paul Scholes then replaced Tom Cleverley before Itay Shechter came on for Agustien in the last three minutes of normal time.
Giggs volleyed wide after Vorm had rushed out to clear, but both sides settled for a share of the spoils.