Both teams are known for their attractive style of play, and each was trying to dominate possession of the ball. In the first 45 minutes, Swansea's passing was more successful, but Arsenal had the best opportunities on goal.
Alex Oxlade-Chamberlain caused problems down the right flank for the Swans, and the young winger was unfortunate enough to see two of his attempts ring off the crossbar.
Arsenal clearly had the momentum in the second half and continued to poke and prod at the Swansea defense. In the 74th minute, the ball bounced dangerously around the penalty area, and Nacho Monreal smashed it into the far corner of the net.
With a 1-0 lead, the Swans had no choice but to push forward, and the Gunners punished their gamble with another goal in the 90th minute. After giving away possession, Aaron Ramsey put Gervinho through on goal, and the winger calmly put the chance away.
Arsenal needed a victory in this match, and the players delivered.

Grades
Santi Cazorla, Arsenal: B
The midfield maestro was back attacking down the center after spending several recent matches on the left wing. He did not appear to be as comfortable orchestrating the attack as he has been earlier this season.
He was still active and moving intelligently, and he was able to create occasional opportunities. But this was ultimately a forgettable match for Cazorla.

Michu, Swansea: C+
Unsurprisingly, Michu had Swansea's best chance of the first half, and the supporters in Wales were shocked to see him do so little with a ball played to his feet inside the penalty area.
The Spaniard has been one of the most lethal goal-scorers in England this year, but this was not apparent today. Michu will also be glad to put this match in the past.
Hi-res-163797610_crop_exact Jan Kruger/Getty Images

Alex Oxlade-Chamberlain, Arsenal: B+
Arsene Wenger trusted the winger with a start, and he repaid his manager with a fine performance. He created more danger in the attack than any other Arsenal player and was unlucky not to get on the scoresheet.
He put an impressive amount of pressure on the Swansea defense, and deserves credit for an excellent outing.

Ashley Williams, Swansea: B
Williams has been one of the more impressive centre-backs in the Premier League this season, and he did nothing to damage his reputation in this match. However, he did not have a spectacular day.
He once again was disciplined in his positioning and distributed out of the back extremely well, but his effort was not enough to help his team keep a clean sheet.

Nacho Monreal, Arsenal: A-
Monreal was not having his finest match, but he was the one to grab the match's only goal. Matches like this can be extremely frustrating, and he deserves a high grade for keeping his composure and knocking in the Gunner's first goal.
It was not the prettiest strike, and it came after a scramble in the the penalty area, but it was ultimately worth a massively important three points for Arsenal.

What's Next
After a week off, both teams will return to Premier League action on March 30.
Swansea will have to try and get a better result against another North London side as they take on Tottenham, and Arsenal will expect to earn another three points when they on Reading.