Moyes saw some calm brought to a turbulent few days when Javier Hernandez's solitary strike at the start of the second half proved enough to defeat Liverpool 1-0 in Wednesday night's Capital One Cup third-round tie at Old Trafford.
The victory earned United a home last-16 encounter with Barclays Premier League strugglers Norwich after a kind draw - one of the few things to have gone well for Moyes since he succeeded Sir Alex Ferguson in the summer.
Moyes' sceptics had a field day following Sunday's 4-1 hammering at Manchester City, which led to claims the Scot is incapable of securing wins in the biggest matches.
For the moment, they have been silenced, as Liverpool striker Luis Suarez's return from a 10-match suspension ended in disappointment.
And, after being told he had now made the best start of any new United manager since Matt Busby in 1946, Moyes claimed he will eventually do it for good.
"Everybody seems to be picking a stat out - I have not won here or I have not done that," he said. "That is one of the good stats.
"I have not had that many good ones. But that is one of the better ones.
"It is is not frustrating. I will sort it. I will fix it. I will turn it round. I have no doubt about that."
Moyes has every reason to look at the world with a good deal more optimism than he did at the weekend.