Scottish Premier League: Motherwell 0 Hibernian 4
The visitors from Edinburgh took the lead in the 28th minute on Friday when a move down the left came to Paul Cairney, who rolled off his defender, drove towards goal and then teed up David Wotherspoon just outside the area.
The 22-year-old Scottish midfielder smashed his shot into the top corner to put Hibernian 1-0 ahead.
Hibernian did not add to their goal tally until the second half when Griffiths earned a penalty after being brought down by Motherwell goalkeeper Darren Randolph in the 64th minute.
The Scottish striker took the penalty himself and made no mistake for his sixth goal of the Scottish Premier League season.
Another penalty 10 minutes later made the scoreline 3-0 when Wotherspoon was fouled on the edge of the area but the referee pointed to the spot, with Griffiths grabbing his second goal of the match to become equal top goal-scorer in the league alongside Motherwell's Michael Higdon.
Hibernian wrapped up the scoring in the sixth minute of second-half stoppage time when Daniel Handling finished off Wotherspoon's lead-up work.
The victory puts Hibernian into second on the league table with 18 points, although they have played two more games than leaders Celtic, who have 20 points.
St Johnstone and Aberdeen can both move ahead of Hibernian on Sunday with victories over Inverness Caledonian Thistle and Dundee respectively.
Motherwell remain sixth with 13 points.