The Swans carved out a surprise 1-0 win against the Gunners at the Emirates Stadium in North London.
France international striker Gomis's headed effort in the 85th minute proved to be the difference between the two sides.
Over the course of the 90 minutes, Swansea had just 32% of the possession, took eight shots of which three were on target, and earned only one corner.
In contrast, hosts Arsenal had 68% of the possession, took 23 shots of which nine were on target, and earned six corners.
Following the match, Gomis took to Twitter to revel in Swansea’s win against Arsenal.
Important win , it was a close game ! I m happy I was able to score the game winning goal to help my team to get the 3 points .I AM JACK...— Bafétimbi Gomis (@BafGomis) May 12, 2015
Victory in North London means that Swansea are now eighth in the Premier League table with 56 points from 36 matches.
The Welsh outfit are just two points off a Europa League place, and could even finish above Southampton and Tottenham Hotspur in the Premier League table.