The Irishman has come in for flak from supporters following a nightmare start to the season that saw them kick off the campaign with four straight defeats.
The Leith outfit were humiliated 9-0 on aggregate by Malmo in the Europa League qualifiers before suffering another mortifying defeat to administration-hit Hearts in the Edinburgh derby.
But Petrie issued a statement on Wednesday offering Fenlon a vote of confidence and it had the desired effect as the team bounced back from a goal down at Rugby Park to register their first win of the new term.
Craig struck both goals in the 2-1 win over Kilmarnock and insisted the Hibs players are fully behind their manager.
He said: "Obviously the players want him to stay. He has brought a lot of us to the club. There have been a lot of changes this season and it was going to take time for us to gel.
"But it is important that when we are not getting results we stick together. We've done that and got a result at Rugby Park. However, there is still work to do but we know we have players capable of getting results in the Scottish Premiership."