John Baird gave the visitors - 11 points adrift at the foot of the table - an eighth-minute lead at Easter Road. However, Griffiths netted four minutes into the second half to earn Pat Fenlon's men a point.
Barry Smith's Dundee are still a long way behind 11th-placed Ross County, but they can be encouraged by a performance that could have deservedly earned them all three points.
Winter break rust appeared to have an effect on the home side in the first half. Hibernian, missing the influential Paul Cairney through suspension, were wayward with their passes and there was no dynamism to their performance. Dundee, in contrast, looked a completely different side to the one that was cut adrift at the bottom of the league prior to the 17-day break.
The first goal was scored before any rhythm could be established but the advantage the visitors held at half-time was more than deserved, Dundee playing with confidence and composure which their hosts could not match. Former Hibs striker Colin Nish was the goal creator.
Much maligned in his time at Easter Road, Nish played the ball through to Steven Milne in a central area before drifting past a crowd of opposing players, controlling the return ball and weighting a perfect through-ball for Baird who coolly slotted past goalkeeper Ben Williams.
A stunned home side should have equalised 60 seconds later. Tim Clancy seemed to repel potential markers as he drifted into the six-yard box but he headed David Wotherspoon's cross awkwardly over the bar.
Jim McAlister was also found lacking five minutes before the interval. The midfielder blazed over after another shoddy example of defending allowed Nish to create a chance through a routine long ball from goalkeeper Rab Douglas.
The Dundee defence had done an excellent job of shackling Griffiths but conceding a free-kick 20 yards from goal was all the invitation the forward needed to level the scores. The Scotland international clipped the ball over the wall and past Douglas at his near post.
The goal brought the crowd back on side but there was no momentum accompanying it. Instead it was Dundee who created the better chances thereafter, with Steven Milne firing at Williams from close range and Nish seeing a shot parried by the Hibernian goalkeeper.
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