Leonardo Da Silva Lopes, Marcus Maddison and Mallik Wilks had each scored to put the home side in front, but the Swans had pegged them back each time before the visitors took a 4-3 lead six minutes from time. However, Eaves had the final say with a goal five minutes into added time as the points were shared.
Head Coach Grant McCann made just the one change to his starting eleven following Tuesday night’s defeat at Blackburn Rovers as Matthew Pennington returned from injury to take his place in the back line. It meant that Robbie McKenzie moved back out to right back with Da Silva going into midfield and George Honeyman dropping down to the bench. Kevin Stewart, who had been out since November with a foot problem, was included amongst the substitutes.
The Tigers made a bright start and created a chance inside the opening two minutes as Maddison’s free kick was headed back across goal by Josh Magennis for Mallik Wilks who sent a header over the bar.
That bright start was rewarded with an opening goal in the sixth minute. Callum Elder’s cross made it through to the far post where Da Silva was unmarked and he beat Freddie Woodman with a low finish.
The lead lasted only seven minutes, though, as Swansea hit back. The visitors made progress down their left and, when a low cross came in, Wayne Routledge was all alone to fire in from eight yards.
George Long made a save from Conor Gallagher’s 20-yard effort and then turned Bersant Celina’s free kick wide as the Swans enjoyed a decent spell, although their centre back Ben Wilmot did pick up a booking for a late challenge on Jackson Irvine.
Gallagher’s looping header dropped just wide of Long’s left-hand post and Kyle Naughton fired into the side-netting as Swansea continued to look the more likely, but there were no further goals before the break.
Pennington glanced a Maddison free kick wide shortly after the restart before the Tigers regained the lead in the 50th minute. It was Maddison that created it with some positive running through the middle and, when his initial shot was blocked and looped up into the air, it was the man on loan from Peterborough United that followed it up himself inside the box to bury the loose ball.
The lead was short-lived again, though, as Swansea levelled five minutes later. The Tigers switched off at a corner as the ball was played low to Naughton and he lashed a shot into the net.
The goal-scoring continued, though, and the Tigers were back in front just after the hour. Daniel Batty’s cross from the right was only cleared as far as Wilks and he found the bottom corner with a left-footed finish.
A double change saw Honeyman and Ryan Tafazolli replace Batty and Maddison as McCann switched to a three-man defence, although they could do little more than stand and watch as a Gallagher shot sailed just over the bar.
Swansea pulled themselves level for a third time 13 minutes from time as Ayew tore down the left before delivering a low ball for substitute Jordon Garrick to convert from close range.
A final change saw Eaves replace Wilks, but it was Swansea that snatched the lead six minutes from time through substitute Brewster.
Woodman scrambled to save from Magennis, and the Tigers would end a remarkable game with an equaliser five minutes into added time. Magennis did well to get a low cross in from the left and Eaves slid in to score from just a few yards out.
Hull City: George Long; Robbie McKenzie, Matthew Pennington, Sean McLoughlin, Callum Elder; Leonardo Da Silva Lopes, Daniel Batty (George Honeyman 66), Marcus Maddison (Ryan Tafazolli 66); Mallik Wilks (Tom Eaves 81), Jackson Irvine ©, Josh Magennis.
Subs Not Used: Matt Ingram, Kevin Stewart, Stephen Kingsley, Keane Lewis-Potter.
Swansea City: Freddie Woodman; Kyle Naughton, Marc Guehi, Ben Wilmot, Jake Bidwell; Jay Fulton (Yan Dhanda 64), Matt Grimes; Wayne Routledge (Rhian Brewster 64), Bersant Celina (Jordon Garrick 73), Conor Gallagher; Andre Ayew.
Subs Not Used: Erwin Mulder, Nathan Dyer, Connor Roberts, Ben Cabango.
Referee: Mr D. Webb.