The Swans ended their three-match losing run with a first Barclays Premier League point against Norwich.
In a thrilling game at Carrow
Road, Michu had fired the Swans ahead after 35 minutes with his 21st goal of the season.
But the hosts were on level terms five minutes later as Robert Snodgrass headed in Elliott Bennett's cross.
The second half promised plenty of thrilling action, and it certainly delivered.
Michael Turner turned home Bennett's free-kick on the hour to edge the hosts ahead, but Luke Moore tapped home sub Angel Rangel's header along the face of goal with 15 minutes to go.
There was plenty of time for both sides to win it, but the best chance fell to Michu, but he fired high over the crossbar from Pablo Hernandez's low cross.
This point, which came following defeats to West Brom, Arsenal and Spurs, moved the Swans onto 41 points with six games to go.
The Swans made two changes to the starting XI. Leon Britton didn't make the trip to East Anglia after his wife gave birth two twin boys - Charlie and Alfie - earlier this week, so Ki Sung-Yueng started in midfield alongside Dutch international Jonathan de Guzman and Michu, who dropped back from leading the line, which meant Luke Moore started up front.
Norwich made one change from the side that lost at Wigan last time out, with keeper Mark Bunn returning from suspension to take the place of Lee Camp in goal.
Mark Bunn (Lee Camp, 15), Russell Martin (capt), Michael Turner, Sebastian Bassong, Javier Garrido, Elliott Bennett, Bradley Johnson, Jonathan Howson (Alex Tettey, 81), Robert Snodgrass, Wes Hoolahan (Grant Holt, 80), Kei Kamara.
Steven Whittaker, David Fox, Luciano Becchio, Ryan Bennett.
Michel Vorm, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies (Angel Rangel, 64), Ki Sung-Yueng, Jonathan de Guzman, Michu, Nathan Dyer (Roland Lamah, 74), Wayne Routledge (Pablo Hernandez, 64), Luke Moore.
Gerhard Tremmel, Garry Monk, Kemy Agustien, Itay Shechter.
The Swans were the first to probe, Michu side-footing his effort wide from 20 yards after Wayne Routledge had picked him out after five minutes.
Two minutes later and the visitors were busy creating another chance as Michu found Luke Moore, and the striker's effort low across goal saw Mark Bunn having to scramble across to collect.
The Swans did manage to beat Bunn in the tenth minute, Michu firing low into the corner only for referee Michael Oliver to rule out the goal due to Luke Moore's challenge on Bradley Johnson.
But Bunn's afternoon was over shortly after, the keeper being replaced by Lee Camp after injuring himself during a clearance kick.
Norwich then went close to opening the scoring just past the 20-minute mark as, following a blocked free-kick, Robert Snodgrass' cross found defender Michael Turner in the box and his shot was superbly pushed out for a corner by Michel Vorm.
It then took a fine block from Ashley Williams to deny Johnson, before the skipper again stretched out a boot to block Russell Martin's effort.
The Swans quickly responded, Moore screwing his 20-yard shot wide before the Swans broke the deadlock.
In the 35th minute, the Swans opted for a short corner, which culminated in Jonathan de Guzman pulling the ball back to Michu, and he blasted past Camp from ten yards.
The Swans were soon pushing for a second, Michu racing forward during a counter attack and sending Nathan Dyer down the right, but the winger's angled drive bounced wide.
The lead didn't last long, however, as Snodgrass headed home after Elliott Bennett's curling cross in the 40th minute.
Alex Tettey then drove high and wide as Norwich went in search of the lead, but both sides went into the break on level terms.
Half-time: Norwich 1 Swans 1
The Swans started the second half as they did the first, and Moore was denied by Camp after Routledge's flicked pass deceived the Norwich defence.
Vorm comfortably dealt with Elliott Bennett's dipping volley as the hosts hit back with a surge of their own, and they eventually took the lead on the hour mark.
Bennett's free-kick dropped towards the back post and the unmarked Turner thundered home to send Carrow
Road into ecstasy.
The Swans had an immediate chance to level, but Michu could only direct his header from Ki's cross straight at Camp.
Michael Laudrup then made two changes with Angel Rangel and Pablo Hernandez replacing Ben Davies and Routledge.
Norwich upped the pressure as the home crowd raised the atmosphere a notch, and Kei Kamara's header just looped over the crossbar.
The Swans almost found themselves two goals down when a deep free-kick was nodded back by Turner, but Kamara was beaten to the loose by Michu, who calmly headed back to Vorm.
Then it took a last-gasp tackle from Tiendalli to deny Kamara a certain goal from point-blank range as the home pressure started to build.
In a brief respite, Moore rose to meet Hernandez's cross, which Camp tipped over before Laudrup's final change saw Roland Lamah introduced in place of Dyer.
Then, just moments later, the Swans got themselves back onto level terms.
Tiendalli's deep cross was nodded back along the face of goal by Rangel, and Moore tapped home from four yards.
The game continued to excite, with skipper Martin drilling a thunderous shot past the post while at the other end Michu sliced wide from a low cross.
The Swans then had a superb chance to win it in added on time, Hernandez working his way into the box before crossing to Michu, but the ball bobbled as the Spaniard struck and the shot flew high into the crowd.
But that was the end of the action, with both sides sharing the spoils.