Phil Jagielka headed over late on as the two teams eventually had to make do with a point.
Here, Sports Mole takes a closer look at the events that unfolded at Goodison Park.
On Target 3
On Target 0
Was the result fair?
Neither team did enough at Goodison Park to merit the three points. Although Everton dominated the possession and were in control of the match for large periods, they rarely troubled goalkeeper Lukasz Fabianski. Swansea actually had the best chance of the match, but Bony fired wide when through on goal. The hosts may feel that they could have done more to win the game after Shelvey was sent off, but Garry Monk's players did well to weather the late pressure and come away with a draw.
Everton saw all of the ball in the first half, yet they struggled to create many goalscoring chances. They seemed to lack a cutting edge and found it hard to get behind the Swansea backline. It was a different story after the break, as the vistors were much more of an attacking threat and put them under real pressure. That all changed the moment that Shelvey was sent off and from then on, there only seemed one winner. However, despite bringing the likes of Romelu Lukaku off the bench, they still struggled and were unable to find their recent goalscoring form as the game finished on level terms.
The Swans are used to dominating possession, but today they were very much second best in that aspect of the game. Throughout the first half they were penned back deep inside their own half and came under a huge amount of pressure. They did manage to create the best chances and Bony probably should have scored early on. There was also a big shout for a penalty when Antolin Alcaraz appeared to handle Shelvey's shot inside the box. Monk must have had some strong words for his players at half time, as they looked a different team after the break, but when they went down to 10 men they had to hold on and grind out a well-earned point.
Sports Mole's man of the match
Ashley Williams: One of the main reasons that Swansea came away with a draw this afternoon was the performance of Ashley Williams. The captain was strong throughout and was rarely beaten in the air. He led by example and his influence rubbed off on his teammates as they battled to keep a clean sheet.
The mistake of the match must go to Shelvey, who was sent off with 18 minutes left to play. The challenge that led to his second yellow card was poor and there were enough Swansea players back to cope with the threat.
Kevin Friend certainly had a busy afternoon. He could have easily given a penalty to Swansea when Alcaraz handled in the first half, but he waved away their appeals. He was forced to hand out seven yellow cards and there can be no complaints by Shelvey about his sending off.
Everton: The Toffees host Lille in the Europa League on Thursday, before returning to league action with a visit to Southampton on Sunday.
Swansea: Swansea's next match sees them take on Arsenal at the Liberty Stadium next Sunday.