The 33-year-old’s game time has been managed carefully since arriving on a free transfer on deadline day.
Cavani hadn’t played competitive football since March prior to moving to Old Trafford and is still making his way back to full fitness.
The Uruguayan came on as a substitute and scored United’s third goal at Goodison Park in injury time to wrap up the three points.
And Red Devils captain Maguire has been impressed with what he’s seen from Cavani in training and backed the veteran striker to score plenty more goals for the Manchester club.
‘It’s great to see Cavani come on,‘ Maguire told MUTV.
‘He worked tirelessly up there and did the dirty work and he got his rewards right at the end. I think he’s going to be a big player for us, he’s going to score goals.
‘He knows where the back of the net is and I’ve seen that in training a few times already.
He’s just getting up to speed in terms of his training and work rate but he’s going to be a big player for us.‘
United have faced plenty of criticism this season for their form in the Premier League which has left them languishing in 14th place.
And Maguire suggested critics actively want the Red Devils to fail because of their past successes.
‘At this club one thing I’ve noticed in my time here – I’ve been here a year and a half – is we are the most talked-about club in the world,’ he added.
‘Why? Because we are the biggest club in the world. People don’t want us to do well. Why? Probably because of the success we’ve had in the past.
‘We have to live up to that, we have to react to it and don’t let the negatives get into our bubble inside the training ground. Sometimes it is difficult for the lads.’