Walsh's kick answered a 20-yard field goal earlier in the overtime by the Packers' Mason Crosby.
Christian Ponder completed 21-of-30 passes for 233 yards with a touchdown for the Vikings (2-8-1), who recorded their first tie since 1978 against the Packers.
Adrian Peterson racked up 146 rushing yards and a score on 32 carries.
He rallied them to 17 straight points, going 21-of-36 through the air for 218 yards and a TD pass.
Crosby kicked a score-tying, 27-yard field goal with 46 seconds remaining to force overtime.
The tie was the first in the NFL since a Nov. 11, 2012, game between San Francisco and St. Louis.