Premier League Preview: Manchester United v Manchester City
Victories over Olympiacos and West Ham, the former overturning a 2-0 UEFA Champions League last-16 deficit to secure United's progression, have served to dampen criticism of the Scot.
However, Moyes knows murmurings could intensify if seventh-placed United again come up short at home against a bitter rival following the recent 3-0 home loss to Liverpool.
While the Old Trafford faithful will be far from satisfied by another game in which their sole aim is to hinder a rival's Premier League title aspirations, a triumph would be a feather in the cap of the United boss.
"We'll go into our next game confident and ready to get a result," said a bullish Moyes after Saturday's 2-0 win at Upton Park.
For City, the game carries similar significance at the start of what will likely prove a season-defining run of fixtures.
Currently six points behind leaders Chelsea with three games in hand, Manuel Pellegrini's men head to their neighbours brimming with confidence after a 5-0 drubbing of Fulham at the weekend.
But City will be aware, too, that the derby precedes trips to Arsenal and Liverpool, which sandwich a tricky home game against Southampton.
Pellegrini will not be able to call on the services of key striker Sergio Aguero, who is another week away from fitness as he continues his rehabilitation from a hamstring injury.
However, Edin Dzeko looks set to be fit after being taken ill before the Fulham game and Stevan Jovetic should also be available having returned from injury for the final eight minutes on Saturday.
"I think that this team doesn't depend just on one striker," said Pellegrini. "Maybe in the last week we had some problems with Aguero and Jovetic.
"Now Jovetic is coming back and I hope Aguero will be next week with the team. If they don't score there are other players that will do it."
Chief among the supporting cast is Yaya Toure, who boasts 16 Premier League goals this term following his hat-trick against Fulham.
Moyes will, therefore, be buoyed to have Nemanja Vidic and Rio Ferdinand available having been forced to deploy Michael Carrick at centre-back versus West Ham.
Vidic is back from suspension and Ferdinand was rested at the weekend.
The pair, so often United's starting pair in recent years, seem certain to battle it out for a spot alongside Phil Jones at the heart of the defence.
At the other end, Moyes will surely deploy Juan Mata behind Wayne Rooney again as Robin van Persie continues to be sidelined.
City head to United following four successive Premier League clean sheets and bidding for a third straight victory at Old Trafford in a row.
Pellegrini's men were also 4-1 winners when the sides met back in September at the Etihad Stadium.