Ole Gunnar Solskjaer's team scored either side of half-time before Colin Kazim-Richards got one back for Wayne Rooney's Championship side.
Tom Heaton impressed on his first appearance since re-joining the club this summer while Jesse Lingard looked sharp after returning from his loan spell at West Ham United despite only returning to training late last week.
With the majority of Solskjaer's stars on holiday after Euro 2020, he picked a team with a mixture of first-team regulars and youngsters as he prepares for the start of the new Premier League season in a months' time.
It was Chong who gave United the lead in the 18th minute, robbing the ball from Max Bird in the penalty area before scoring at the second attempt after his first effort was saved by Derby goalkeeper Kelle Roos.
Chong is set to spend next season away from Old Trafford after agreeing a season-long loan deal with Championship side Birmingham but took his chance to impress after being given the opportunity to stay at United during preseason.
Solskjaer made nine changes at half-time with only centre-backs Tuanzebe and Mengi keeping their places.
Pellistri, 19, spent the second half of last season on loan at Alaves in Spain after joining United from Penarol for €10 million last summer.
Lingard, involved in the build up to Pellistri's goal, almost created another for Hannibal Mejbri before rattling the crossbar with a fierce drive from the left-hand corner of the penalty area. Kazim-Richards got Derby's consolation after beating Lee Grant from 20 yards.
United next head for a week-long training camp in the UK before travelling to London for the second preseason friendly against QPR on Saturday.