The pair go head-to-head at the Etihad Stadium on Sunday in the first Manchester derby of a new managerial era for both City and United.
They have not been in opposing dug-outs since 2005, when Moyes' Everton took on Pellegrini's Villarreal in a Champions League qualifying round tie.
The Chilean emerged victorious on that occasion, securing single goal victories in both legs to go through.
The scoreline does not quite tell the story of the contest though as Duncan Ferguson mysteriously had a late header in the second leg ruled out by Italian referee Pierluigi Collina that could have taken the tie into extra-time as Diego Forlan did not score Villarreal's winner until stoppage time.
Everton's performance was not put into true perspective until later in the season, when Villarreal swept into the semi-finals, where they were beaten by Arsenal.
But the manner of that defeat still bugs Moyes.
"It did rankle because we scored what we thought was a legitimate goal to take it into extra-time and it didn't count," said the Scot.
"Villarreal did have a really good team. They got to the semi-final of the Champions League that year so for us to run them really close gave me an idea of what a good side we were as well."
The teams have changed now though, so there is little relevance from that occasion to the one they face on Suinday.
Neither is Moyes taking much comfort from an impressive personal record at the Etihad Stadium, where he has won on four of his last six visits, losing on only one occasion.
"You remind quite often how difficult it is for me to get results at some other places so I wouldn't be the one shouting about it," he said.
Nevertheless, it is a game of some significance, not least because it marks the end of that horrific run of fixtures Moyes highlighted before the campaign even began.
That United go into the contest on level terms with their Mancunian neighbours offers an opportunity to take a fairly sizeable stride forward.
"We've had the hardest start of all the top clubs in the Premier League so we had to make sure after these games we had a decent points total," said Moyes.
"After the City game we'll have played two or three of our biggest rivals and they'll probably have each other to play at different times."
Although Moyes has played largely the same team in successive wins over Crystal Palace and Bayer Leverkusen this week, it is difficult to envisage the Scot making significant changes this weekend.
The experience of veteran midfielder Ryan Giggs may be utilised given the Welshman was not even on the bench in midweek.
However, central defensive duo Rio Ferdinand and Nemanja Vidic look certain to partner each other for the third time in a week for the first time since 2010 and Marouane Fellaini should also retain his place after a tidy first start against the Germans.
"Marouane played well the other night," said Moyes.
"I thought the supporters felt there was something there we could work with and that he could help the team.
"We have a side which is full of creative players.
"We make lots of chances and scored many goals last season as well.
"What we have to do is make sure we give ourselves a chance by not conceding many."
A veteran of similar confrontations on Merseyside and in his native Glasgow, Moyes cannot put one derby ahead of another.
"It would be an insult to the clubs of Merseyside and Glasgow to say the Manchester one was bigger," said Moyes.
"Derbies are important to everybody, whatever city you are in. Everyone is aware of it."