Substitute Griffiths struck in the fourth minute of time added on at the end of the match - seconds after Billy Clarke looked to have rescued a deserved point for the visitors with an equalising goal.
In the first ever meeting between the two sides, Wolves rode their luck after Bjorn Sigurdarson had given them a seventh-minute lead when he headed home Kevin Doyle's cross.
Crawley could easily have wilted after that early blow but they were unlucky not to be back on level terms by half-time.
Ikeme then saved from Adams and Clarke at the start of the second half as the Red Devils proved to be far from overawed in the lofty surroundings of Molineux.
Clarke eventually made Crawley's persistence pay 30 seconds into added time when his low drive beat Ikeme and went into the back of the net via the base of the post.
It should have earned Richie Barker's boys a hard-earned share of the points but Wolves surged forward in one last attack and won a penalty when Kyle McFadzean was adjudged to have handled Kevin McDonald's cross into the area.
Griffiths held his nerve to convert his second penalty in successive home games, opting for power rather than finesse.
Elsewhere, Freddie Sears' second-half equaliser for Colchester denied Carlisle their first win of the season as an entertaining League One fixture at the Weston Homes Community Stadium finished in a 1-1 draw.
Carlisle took a fourth-minute lead when left-back Matty Robson lashed home a fine low shot from 20 yards which flew past home goalkeeper Sam Walker and into the back of the net.
Lee Miller nodded wide for the visitors from eight yards before Mark Gillespie saved Jabo Ibehre's fierce effort and Colchester youngster Tosin Olufemi's curling, first-time shot rattled the crossbar as the contest continued to ebb and flow.
Miller and Robson both went close for Carlisle as did Ibehre for Colchester, for whom Sanchez Watt fired just wide early in the second half before Craig Eastmond also went close.
Walker had to save Miller's shot at his near post and the visitors then had a goal chalked out for offside after Liam Noble had put the ball in the net.
Gillespie palmed Sears' shot over before Sears levelled with 19 minutes to go when he blasted home a half-volley after Gavin Massey had controlled Watt's clever pass.
Gillespie palmed over substitute Alex Gilbey's header late on as the points were shared.