Thriller ends in agony for DKs.
The visitors ran in five tries to earn two bonus points but a charged-down conversion in the dying minutes proved costly.
Westoe began strongly and Matt Mellish slotted over a firstminute penalty with Samoan full-back Lomi Faatau adding a fourth-minute try on his debut.
DKs recovered and took the lead thanks to tries from skipper Ed Parry and Stefan Shillingford, Gareth Bown adding a consolation.
The lead changed hands again before the break as tries from John Younghusband and winger Graeme Haswell handed the home side a 20-12 lead at the interval.
DKs had the benefit of the slope in the second half and a Bown penalty was followed by tries from Matt Farrington and full-back Simon Fletcher.
Westoe bounced back with replacement Joe McKenzie and back row Oliver Cracknell crossing before Fletcher bagged his second of the game with 80 minutes on the clock.
That try in the corner edged DKs to within two points of their hosts but as Bown ran up to take his conversion, the ball toppled over and the kick was