Griffiths took his tally for the season to five before Sako saled the win in the final minute as United slipped to a sixth successive league defeat.
But this latest loss was tough on David Weir's team who had dominated the game for long spells in the first-half.
They had more than enough chances to build up a commanding lead before Griffiths struck in the 66th minute.
The Scotland international bundled the ball over the line at the second attempt from Sako's left-wing cross after United goalkeeper George Long had saved his first effort.
Sako then got in on the goalscoring act himself in the 90th minute with an unstoppable 30 yard drive after a neat pass from former United midfielder Kevin McDonald.
United only had themselves to blame for this latest loss as they should really have taken a lead into the interval only to be frustrated by the Wolves keeper Carl Ikeme.
He did well to deny Florent Cuvelier in the eighth minute and then 60 seconds later frustrated Febian Brandy.
Brandy tested Ikeme again in the 27th minute following good work by Marlon King before Cuvelier failed to hit the target when well placed on the half hour.
Brandy then headed a King cross wide in the 52nd minute and Griffiths and Sako took full advantage to punish them and earn Wolves a seventh win in their last eight league games.