Dick Advocaat secured his first point of the new season as Sunderland boss, as a Jermaine Defoe equaliser cancelled out Gomis's strike.
The Wearside faithful yearned for more commitment from their players, and this was evident early on through Lens who was their main focal point of attack, and it was his link-up with Defoe which almost saw the opening goal, but the much-travelled Premier League striker could not get his toe in after the Dutchman's cross.
After performing abysmally in their opening games, it was no surprise that Swansea took scored on the stroke of half-time through the in-form Bafetimbi Gomis.
Defoe equalised in the 62nd minute with a typical strike to earn the Black Cat's their first point of the new campaign.
And they could have won it late into injury time but Coates could not direct his header into the goal following a Lens corner.
Sunderland: 1 (Defoe 62)
Swansea: 1 (Gomis 45)
Attendance: 39,198
Match report by Joe Baker