Swansea missed a chance to move into the automatic promotion places after being held 1-1 by Hull.
The Welsh side broke the deadlock through Mark Gower in the 63rd minute but Hull levelled seven minutes later courtesy of a Corry Evans strike.
Gower's 20-yard drive put the Swans in the driving seat as they sought to step up their bid for promotion.
But the Tigers quickly restored parity when Evans finished smartly from inside the box.
Moments later James Chester nearly put Hull ahead but his header from Robert Koren's pass went wide.
Simpson certainly made an impact as with 13 minutes left he was denied by Swansea goalkeeper Dorus De Vries, who was making his 200th league appearance