Hitchcock leveled matters before Bradley Dack struck on 84 minutes to give Peter Taylor's troops a 3-2 advantage going into the final stages.
However, there was yet more drama as Hitchock equalised just two minutes later, before pouncing in the dying moments to snatch all three points for Steve Evans's men.
Consequently, United extend their unbeaten streak to 16 matches - 12 of which have been victories - as the Millers leapfrog Leyton Orient into third place.
In contrast, Orient's winless run extended to five games as the Londoners were held to a 1-1 draw with Sheffield United at Bramall Lane.
Dean Cox had fired the O's into a 1-0 half-time lead, but Jamie Murphy was on hand midway through the second half to level matters.
MK Dons beat Coventry City 2-1 at Sixfields to move within three points of Peterborough, who occupy the final playoff place.
Carl Baker equalised for the hosts on 57 minutes following Bamidele Alli's first-half opener, but Izale McLeod was on hand to fire the Dons ahead once more midway through the second half.
At the bottom of the division, Shrewsbury Town boosted their survival prospects by earning a slender 1-0 win over bottom-placed Stevenage at New Meadow.
Jon Taylor's second-half strike proved enough for third-from-last Salop to move within two points of safety ahead of the remaining fixtures in England's third tier
Results in full: Bradford City 2-3 Oldham Athletic, Brentford 3-1 Notts County, Bristol City 1-1 Preston North End, Carlisle United 1-0 Swindon Town, Colchester 1-2 Tranmere Rovers, Coventry City 1-2 MK Dons, Crawley Town 1-2 Crewe Alexandra, Gillingham 3-4 Rotherham United, Port Vale 1-0 Walsall, Sheffield United 1-1 Leyton Orient, Shrewsbury Town 1-0 Stevenage, Wolverhampton Wanderers 2-0 Peterborough