But they are likely to face a sterner test against Jose Mourinho’s Chelsea, who started their campaign with consecutive home wins against Hull City and Aston Villa.
Since being confirmed as Sir Alex Ferguson’s successor, Moyes has had to wait more than 100 days for his first competitive fixture in front of the club’s supporters.
And although it is a match United will enter without a significant close-season signing – something they have been pursuing strongly – Moyes is still excited.
He said: “There have been a lot of things I have been looking forward to – like taking the team on tour and leading them out at Wembley.
“But to do it at Old Trafford for the first game against Chelsea is a thrill for me, it really is.”
With both sides set to seriously challenge for the Premier League title, the fixture will have plenty riding on it, with neither camp willing to concede early ground to their rivals.
An intriguing sub-plot is the future of want-away Manchester United forward Wayne Rooney.
Rooney has submitted two transfer requests in the last three years and is a transfer target for Chelsea, who have had tfo formal bids turned down by United.
Mourinho claimed Chelsea would not renew their interest until after the match had finished, in the interests of being professional and respectful.
Moyes has repeatedly said Rooney is not for sale and revealed he may start against Mourinho’s men.
“Wayne’s got a good chance of playing. He has [a] good chance of starting [also],” Moyes said.
Brazilian defender Rafael [hamstring] is a certainty to miss, as is Darren Fletcher [illness] and Nick Powell [leg] for United.
Ashley Young [ankle], Nani [groin] and Chicharito [hamstring] are unlikely to feature.
Chelsea could consider themselves fortunate to have defeated Villa 2-1 on Wednesday, with defender Branislav Ivanovic – who headed the winner with 17 minutes remaining – only given a yellow card after catching Christian Benteke with an elbow.
The Blues have not lost in their last 10 Premier League fixtures – a run that included a 1-0 win at Old Trafford in May.
While United’s home Premier League record is simply outstanding – they have won 51 of their last 59 home matches, losing just five – two of those defeats came against Chelsea.
The two sides played each other five times last term, with Chelsea knocking their rivals out of both the FA Cup and the Capital One Cup.
Mourinho’s only fitness concern is David Luiz, who is a doubt to feature due to a hamstring injury.