McTominay was one of only two survivors from the EFL Cup semi-final defeat to Manchester City on Wednesday and the midfielder – captaining the Red Devils for the first time – headed his side in front after just five minutes.
Eric Bailly and Juan Mata squandered good chances to extend United's lead before the interval, while Dean Henderson had to be alert to thwart Adam Masina.
United rarely threatened a second during a dismal second half but they saw things out with the minimum of fuss to inflict a 10th straight defeat for the Hornets at Old Trafford.
The hosts wasted little time stamping their authority on the tie, McTominay heading home his fourth goal of the season from Alex Telles' outswinging corner in the fifth minute.
United goalkeeper Henderson was out quickly to deny Masina soon after, while Bailly flashed a header wide from another dangerous Telles ball into the penalty area.
Mata fired straight at Daniel Bachmann following a superb flicked pass from Donny van de Beek as United ultimately failed to add to their advantage before half-time.
Solskjaer brought on Marcus Rashford and Anthony Martial with just over 20 minutes remaining in a desperate bid to inject some life into the home team’s stuttering attack.
Rashford should have put the seal on the win, but his low effort after a fine run was too close to Bachmann.