United were made to sweat for the three points against Villa at Old Trafford as the visitors pressed for a late equaliser.
Fernandes’ second-half penalty was enough for United to clinch victory after Bertrand Traore had cancelled out Anthony Martial’s header.
The Portuguese playmaker now stands on a phenomenal 11 goals and seven assists in just 16 Premier League matches and has catapulted United up the table.
Victory against Villa puts United level on 33 points with leaders Liverpool, who are only above Solskjaer’s side on goal difference.
United are 10 games unbeaten in the league and have won eight times in that spell to leap up the league and enter the title mix.
But Fernandes has warned that United must begin to be more clinical with their chances if they truly want to rival reigning champions Liverpool for their crown this term, insisting their “mistake” against the Midlands outfit was not scoring more goals.
Solskjaer said post-match: “I didn’t enjoy the last 10 minutes that much. I think we should have seen the game out in a better way.
“It seemed like it was a cup final or the last game of the season. We need to learn how to play out games better when we’re in the lead.”
And Fernandes agreed: “I agree with that because against Leicester we conceded a goal at the end.
“The only mistake we made today was we had more chances to score again and maybe we have to close the game more quickly. We don’t score the third one and they press us until the end.
“We knew they [Aston Villa] play really well. They have qualities and are doing well in the league.
“We did well and created more chances than before but scored less goals. The most important thing is three points though.”
Solskjaer also declared after the win over Villa: “We created chances. It’s always going to be a physical game. We know that they’ve improved massively and they gave us some challenges.
“There were a few times in that box that you were a bit worried. We didn’t stop the crosses well enough, when they put crosses in the box they were always dangerous.
“We made some fantastic blocks, some saves. Delighted with the three points obviously.
Woodward must consider Sir Alex Ferguson’s Man Utd transfer advice
Man Utd fans slam Ole Gunnar Solskjaer for Donny van de Beek snub
Two Man Utd stars picked out who are ‘nowhere near full potential’
“Maybe not just Paul [Pogba] but we were too keen on playing the killer pass. We know they’re going to drop off and there’s other spaces in behind them that we should have used.”
“Don’t get me wrong I’m delighted with the three points and very happy with the performance. But there’s always things we need to improve on.
“It’s early on in the season and we shouldn’t get too carried away with three points. It’s not a cup final yet – but those three points extra, they are important.”
On United’s title prospects, the Norwegian boss added: “We’ve improved, we’re getting better and the league and the season is going to be so tight anyway.
“There’s going to be different and difficult games and strange results. We’ve just got to keep working and improving as a team.
“Since project restart started, I think we’ve been a very consistent team. Every time you win a game, of course you take one step further. It’s three points in total.
“You’ve just got to accumulate the points. The first game is just as important as the last game. They all count the same.”