The Blue Toon looked on course to add another victory to their impressive record at Broadwood – having won on six of their previous eight visits – when goals by Russell McLean and Grant Savoury put them two up after just 26 minutes.
But a penalty converted by Goodwillie five minutes into first-half stoppage time gave the hosts a lifeline, and the Clyde skipper struck again early in the second half to earn the home side a point.
Peterhead arrived hoping to open up a gap on Clyde, in the League 1 relegation play-off spot a point behind Jim McInally’s side.
Clyde were dealt a blow when Ross Cunningham was stretchered off with a back injury after an awkward landing, although the lengthy delay for treatment would later work to their advantage.
The Bully Wee then suffered two further setbacks in the shape of a brace of Peterhead goals in the space of six minutes.
The first came on 20 minutes when skipper Scott Brown’s cross found McLean, whose emphatic finish went in off the underside of the bar.
Six minutes later Savoury doubled the visitors’ advantage, firing past Neil Parry after McLean rolled the ball to him.
A McLean effort was deflected just wide and Savoury sent another shot just over as Peterhead looked to add to their lead.
But the game’s turning point came just before the interval, deep into the time added on for Cunningham’s injury.
Referee Peter Stuart pointed to the penalty spot after Goodwillie went down under the diving challenge of the outrushing Long and the former Scotland striker calmly rolled home the spot kick.
That goal gave Clyde a huge lift and they were back on level terms seven minutes after the restart as Goodwillie got free on the right and cut inside Flynn Duffy before steering his finish beyond Long.
Goodwillie then almost put Clyde in front on the hour with a strike from the edge of the box, but Long dived to turn the ball for a corner.
And Peterhead were also inches away from regaining the lead as McLean beat Parry with his strike only to see the ball crash off the crossbar.