The visitors handed out the festive presents with own goals from goalkeeper Craig Mawson and captain Tony James.
Dean Moxey and Sean Devine compounded the misery for Hereford who failed to make an impact on the game.
Exeter were ahead in the 12th minute. Dean Moxey's long ball forward picked out Andy Taylor, whose shot was initially blocked by Hereford goalkeeper Craig Mawson before he palmed the loose ball into the back of his own net.
Hereford attempted to respond and Mark Robinson struck a low strike past the post from the edge of the box.
Jamie Pitman's free-kick then picked out Tamika Mkandawire inside the box for the visitors but his close-range shot was blocked by Taylor.
On the stroke of half-time City made it two. Scott Hiley floated in a fine deep cross from the right which was flicked on by Jake Edwards and teenager Moxey drilled the ball home at the far post.
The Grecians stretched the lead five minutes after the restart. Hiley's long ball should have been cleared by Mkandawire, but the defender misjudged the ball and left Devine free to run on goal and tuck the ball past the goalkeeper.
It came as no surprise when the fourth came on the hour mark. Taylor found Devine inside the box and when he drilled a low shot across the face of goal Tony James steered the ball into his own net from close range.
Strangely the visitors enjoyed their best spell of the game when the match was well beyond them.
Mkandawire headed the ball into the arms of the goalkeeper and substitute David Brown shot wide for the Bulls.
But Exeter were always comfortable and fully deserved to take maximum points.