Despite failing to pick up a victory since the opening day of the season, it was the Blades who began the brighter, with David Weir's men enjoying a monopoly of possession but failing to test goalkeeper Carl Ikeme.
However, the Nigeria international was called into action on the half-hour mark when he was forced to produce a smart save from Febian Brandy, who had raced clear of the Wolves defence.
Kenny Jackett's men began to develop a foothold in the clash, without forging the clear-cut opportunities needed to open the scoring before the break.
The hosts emerged as the stronger team in the second half and began replicating the standard of performance which has seen them ascend to third in England's third tier - and it was not long before their dominance was rewarded.
In-form marksman Griffiths opened the scoring by bundling home Sako's low cross on 66 minutes.
Jackett thought he saw his team double their advantage moments later with Dave Edwards scoring, but his strike was chalked off for handball in the build-up.
The visitors struggled with the same creative problems which plagued them throughout the opening 45 minutes, and Sako put the result beyond doubt in stoppage time, smashing from range to secure the three points for Wolves.