The Cherries twice led on home soil, with Dominic Solanke and Justin Kluivert on the scoresheet, but Fernandes registered a brace, including one from the penalty spot, as the points were shared.
The result has left Man United seventh in the Premier League table, level on points with sixth-placed Newcastle United and 10 points from Tottenham Hotspur in fifth, while Bournemouth stay 12th, now boasting 42 points from their 32 matches this term.
Bournemouth had a half-chance in the third minute when Solanke climbed above Willy Kambwala, who was making his second Premier League start for the Red Devils, to meet a cross from the right, but the Man United centre-back managed to block the ball behind for a corner, which was ultimately cleared.
The Cherries had another opportunity in the seventh minute when Ryan Christie advanced into the Man United box before delivering low into Solanke, but Harry Maguire did brilliantly to clear ahead of the forward.
Bournemouth managed to make the breakthrough in the 16th minute, with Solanke working his way past the teenager Kambwala, who slipped at the vital moment, before picking out the bottom corner with an impressive strike from just outside the penalty box.
Marcus Rashford hit the side-netting in the 18th minute with a powerful strike following a mazy run, with Man United looking to hit back at the Vitality Stadium.
Red Devils goalkeeper Andre Onana then made a smart save down the other end to deny Milos Kerkez, who had been allowed to break into the away side's penalty box, before Luis Sinisterra sent one wide of the far post.
Bournemouth were firmly on top, with Christie firing just over the crossbar in the 28th minute, before the attacker was denied by Onana two minutes later.
Man United were level against the run of play in the 30th minute, though, with Fernandes smashing the ball into the back of the net from inside the box after a cross from Alejandro Garnacho had been deflected into his path.
Bournemouth came close to regaining the lead in the 34th minute through Dango Ouattara, but his effort was just wide of the far post, with the visitors given another let-off at the Vitality Stadium.
The Cherries did score a second in the 36th minute, though, with Kluivert finding space between Diogo Dalot and Kambwala before smashing the ball into the bottom corner of the net.
Kerkez then headed against the crossbar in the 43rd minute before nodding the rebound over, with the 20-year-old somehow being allowed a second opportunity by Man United's defence.
Onana made a brilliant save to prevent Kluivert from making it 3-1 in first-half stoppage time, before Fernandes struck one against the crossbar down the other end in the closing stages of the opening period, with Bournemouth leading 2-1 at the half-time break.
Amad Diallo was introduced for Man United at the interval, with Garnacho departing the field, but it was more of the same at the start of the second half, with Bournemouth on the front foot.
Kluivert danced his way into the away side's penalty box in the 55th minute, but the forward was crowded out at the vital moment, with Man United coming under more pressure.
Kambwala then did brilliantly to clear ahead of Solanke just before the hour, with the striker having the chance to tap a low Kerkez cross into the back of the net from close range.
Man United were awarded a penalty in the 64th minute when Adam Smith handled inside the box, and Fernandes stepped forward to net his second of the contest and level it up at 2-2.
Solanke struck over the away side's crossbar in the 67th minute, and the response from Bournemouth was strong, with the Cherries looking to move ahead for the third time in the match.
Kambwala cleared a dangerous Kerkez cross behind for another corner in the 84th minute, before Max Aarons struck wide of the post one minute later, with the hosts on the front foot.
Amad volleyed wide of the Bournemouth post in the 88th minute, before the home side were incredibly awarded a penalty in the 95th minute, with Kambwala fouling Christie, but it was changed to a free kick following a VAR check, as the contact took place outside the box.
Enes Unal stepped forward, but his set piece hit the wall and went behind for a corner, which Man United cleared, with the points being shared at the Vitality Stadium.