Supporters heading south were affected by a long build-up of traffic near Stoke-on-Trent after the incident on Saturday afternoon.
Highways England said two lanes were blocked between junctions 15 and 14, prompting fears many would not make it to St Andrew's in time for the 3pm kick-off.
One of the lanes had reopened by 1.30pm and the motorway was fully cleared just before 3pm, a spokesman said.