Michael Smith's eighth goal of the season after 57 minutes, from a superb free-kick by Bolton old boy Matt Taylor, threatened to give the Cobblers a fourth successive victory.
Taylor was involved again in Bolton's controversial 75th-minute equaliser when adjudged to have handled David Wheater's header by referee Richard Clark.
Adam Le Fondre, earlier denied an equaliser by Adam Smith's fine save, thumped home his fourth goal in three games to bring the teams level.
Smith came to Town's rescue moments later, tipping over Darren Pratley's header.
Bolton, scorer of eight goals in their previous two outings, were not to be denied a third successive success though.
Andrew Taylor, twice involved in the build-up, provided the assist with a fiercely-driven cross and Morais slid in at the far post to register his first goal for the Trotters eight minutes from time.
There was time for even more controversy when John-Joe O'Toole's equaliser was disallowed for offside in the final minute of stoppage time.