Former Red Devils skipper Bruce, now in charge of Hull, has watched Moyes struggle all season with the task of succeeding Sir Alex Ferguson, with Sunday's 2-2 draw against bottom club Fulham the latest disappointment.
With their title defence stalled and a Champions League berth now looking unlikely, Moyes is facing a battle to prove his credentials.
But Bruce, who once harboured his own ambitions to replace Ferguson, thinks he can succeed if United stick by their six-year contract with the former Everton boss.
"It's particularly tough for David, but make no mistake, they'll turn it around," said Bruce.
"Even the really top class managers like David need time to stamp their authority on it.
"All of us in the game knew that whoever was going to follow Sir Alex was in for a difficult time.
"David has found it difficult, but given time, with the experience he's got, he will turn it around, I'm convinced of that.
"I'm sure Manchester United will give him time
In their past and their history they've always done that and I'm sure that will never change."
Moyes' inability to overhaul the squad last summer is seen as a key reason for his current travails, but the acquisition of record signing Juan Mata in January hinted at better things.
Bruce, for one, never expected Moyes to revamp Ferguson's title-winners inside just one season.
"We all hope to be given the time because it's difficult to turn things around in weeks," he said.
"You need to get your own team together, to have your beliefs and principles.
"With transfers windows now you can't turn it around overnight, you've only got a certain time to bring new players in and let players out.
"When any club is in transition it is always difficult and that's normal."
Source : PA