The 23-year-old - signed from Wolves in January - opened the scoring in the 12th minute of Saturday's clash with his first goal at Celtic Park, a volleyed effort from an Emilio Izaguirre delivery.
Charlie Mulgrew doubled the advantage with a delightful flick from a Griffiths corner 10 minutes later, before the man of the moment capitalised on some questionable defending to hit the hosts' third just short of the hour mark.
The victory, which equals the clubs biggest in the league this season, maintains Celtic's 21-point lead over second-placed Aberdeen, who picked up a 1-0 victory over 10-man St Johnstone.
Ryan Jack's 25-yard strike gave the hosts an early lead at Pittodrie, before substitute Steven MacLean was given his marching orders at the death for a second bookable offence.
James McFadden rounded off the scoring for Motherwell in the 74th minute - a deserved strike given he provided the assists for Iain Vigurs, Lionel Ainsworth and John Sutton's earlier efforts.
Callum Paterson's 69th-minute header proved little consolation as Hearts fell to back-to-back defeats.
The victory pulls Danny Lennon's men level on points with their opponents.
