Maguire, who has endured a difficult start to the season, scored to help Solskjaer’s side clinch an emphatic win at St James’ Park on Saturday.
Manchester United fell behind through Luke Shaw’s early own goal but Maguire headed home the equaliser on 23 minutes.
Despite dominating from then on, United struggled to find the back of the net until the final few minutes when Bruno Fernandes, Aaron Wan-Bissaka and Marcus Rashford all scored.
‘Of course the last result [a 6-1 defeat to Tottenham] made [today] even bigger,’ Solskjaer said.
‘I thought we showed great resilience and great character to come back. I thought we handled that setback really well and were led by a very inspirational captain.’
On Maguire, Solskjaer added: ‘I thought he was excellent. He scores a goal and he leads by example.
‘He’s always a very good character around the place and I’m very happy for him because he’s had a couple of difficult weeks since the last game for us.’
Manchester United midfielder Bruno Fernandes, meanwhile, praised his team’s performance after they clinched their second win of the Premier League season.
‘Today was about winning and not the performance, but we got both together today.’
Following their victory over Newcastle, Manchester United are now 14th in the Premier League, seven points behind leaders Everton.