The Blues have been embroiled in the furore over referee Mark Clattenburg's alleged inappropriate comments to John Obi Mikel, but they looked set to claim the spoils when Victor Moses nodded in his first league goal for the club in the 61st minute.
Swansea looked like they would be made to pay for their inability to craft clear-cut chances during a first half they had the better of, but Hernandez seized on Itay Shechter's pass to fire low beyond Petr Cech with three minutes remaining.
Branislav Ivanovic, back from suspension, made a critical early intervention for the Blues to block Angel Rangel's pull back and deny Michu an effort on goal as Swansea started smartly.
It was wingers Wayne Routledge and Hernandez who were at the heart of many of Swansea's best moment and they were involved in a number of fine break-outs, one of which saw Mikel, who turned in a fine performance given the storm he has found himself at the centre of, make a brave block as Ki Sung-yueng fired at goal.
Chelsea highlighted their threat at the other end as Leon Britton cleared off the line from Fernando Torres' near-post header, which narrowly evaded the incoming Gary Cahill.
Moses' driven cross was then parried by Gerhard Tremmel, making his first Premier League start of the season, who also saved a weak follow up header from Torres.
Chelsea stepped it up after the break and Hazard cut inside to get away a low shot that Tremmel held well to his right, before Moses wasted a superb opportunity by heading over from Torres' cross.
But Swansea fell behind just after the hour mark. Tremmel had saved Hazard's free-kick, but from the resulting corner Moses flicked Cahill's header in off the post.
Swansea pressed as Chelsea looked to preserve their advantage, and a deserved leveller finally came from Hernandez's placed effort before Graham was denied a winner by Cahill's excellent block.
Source: PA
Source: PA