Davide Petrucci and Ryan Tunnicliffe scored in each half as the Reds cancelled out goals from County's Kevin Luckassen and Alex Cooper in front of 4,400 fans at the Global Energy Stadium, formerly known as Victoria Park.
The most northerly team in the Scottish Premier League, County adapted quickest to the unusually hot conditions, taking the lead through Luckassen's driven shot after just five minutes. Bebe came close to a rapid response for United, however, when he cut inside and unleashed a shot that smashed against the underside of the crossbar.
The Reds were therefore made to wait a further 20 minutes or so before getting back on level terms, Petrucci powering a free-kick past County keeper Mark Brown from 25 yards out.
The Italian goalscorer was instrumental when United approved as an attacking force in the second period, although it was the hosts who again edged in front when substitute Cooper swivelled inside the area to beat Sam Johnstone in the 57th minute.
Seven minutes later, the Reds equalised for the second time when Tunnicliffe combined well with Federico Macheda before converting a close-range opportunity.
That proved to be the end of the scoring, partly because Johnstone was on his toes to prevent Dutch forward Luckassen and also Switzerland-born full-back Mihael Kovacevic snatching a late winner for the Staggies.
Honours were therefore even after an entertaining contest, in which the young Reds looked sharp