Romelu Lukaku scored for the second time in as many games as United won the first ever Manchester derby to be played on foreign soil.
The Reds winning Tour run continued in Houston as Lukaku and Marcus Rashford - paired up front together for the first time - hit a quickfire double shortly before the break.
The two sides had been scheduled to meet during last year's pre-season schedule, only for the match in Beijing to be called off due to an unfit pitch.
For United, it was a third win from three matches in the US following the thrashing of LA Galaxy and the narrow, fiery 2-1 win over Real Salt Lake.
Ander Herrera went close from distance inside the opening five minutes, and Henrikh Mkhitaryan then had a snap-shot pushed away by new City keeper Ederson.
David de Gea twice saved well from Raheem Sterling, before Chris Smalling recovered well from a slip to block from Patrick Roberts and Sterling again.
United made the decisive breakthrough eight minutes shy of the interval, however, as our £75m signing showcased the extent of his impressive repertoire.
Paul Pogba's sublime outside-of-the-foot pass picked out Lukaku, who outpaced the advancing Ederson, knocked the ball around him and slammed home a brilliant finish from an acute angle.
Tow minutes later, United moved 2-0 ahead through Rashford, who fired in from close range after excellent work from Mkhitaryan in the build up.
Despite the usual raft of changes from Messrs Mourinho and Guardiola at the interval, United continued to keep up the pressure and could've moved further ahead by the hour mark.
Rashford went for the spectacular and forced a good save from Ederson, and Lukaku then headed wide before he later rattled the crossbar.
City youngster Phil Foden went close with a lob at the other end, whilst Leroy Sane was narrowly off-target with a strike from distance.
United substitute Phil Jones was denied a rare goal by Ederson's incredible triple save from a corner late on, but the match - and with it the bragging rights - was already wrapped up.
United: De Gea (Romero 46); Valencia (Fosu - Mensah 78), Lindelof (Bailly 46), Smalling (Jones 46), Blind (Darmian 46); Mkhitaryan (Carrick 62), Pogba, Herrera (Fellaini 62), Lingard (A Pereira 77); Rashford (Martial 62), Lukaku.
City: Ederson; Walker, Adarabioyo (Mangala 46), Kompany (Stones 46), Fernandinho; De Bruyne (Otamendi 46), Yaya Toure (Diaz 46); Sterling (Nasri 46), Roberts (Sane 46), Foden (Zinchenko 75); Aguero (de Jesus 46).