The win will be sweet revenge for the Northern Irish team, who were beaten 7-0 at the same stage of last year's competition by the Reds. Joe Rothwell (2) and James Wilson netted in that rout but were unable to get on the scoresheet this time around, despite Paul McGuinness' side enjoying the lion's share of possession.
An injury to defensive mainstay Nicholas Ioannou disrupted the pattern of the game and Tyrone took full advantage, scoring a goal in each half. Ioannou was taken off on a stretcher with what appeared to be a painful muscular problem with midfielder Paddy McNair being introduced.
Wilson and Sam Byrne had efforts but Jamie Glackin unleashed a fine right-foot shot into the top corner of Pierluigi Gollini's net to open the scoring just before the break. After Byrne fired across goal for United, a free-kick was headed down for Cathal McShane to bury a smart finish.
Despite a patchwork defence of their own, Tyrone held out stoutly thanks to a physical performance with midfielder Gary Henderson particularly impressive. For United, Wilson worked hard and one superb run created a chance that went begging while Ben Pearson showed some neat touches in midfield. Nonetheless, the Reds will need to improve against Revo Express on Monday.
United: Gollini; McConnell (Harrop), Grimshaw, Ioannou (McNair), Rowley; Pereira (Goss), Weir, Rothwell, Pearson; Byrne, Wilson.