Fernandes' first goal, assisted by Alejandro Garnacho just after the half-hour mark, cancelled out Dominic Solanke's 16th-minute opener. And after Justin Kluivert restored the home side's lead for the break, the Reds' Portuguese captain popped up in the second period to net a penalty.
A spot-kick was awarded for the second time in the game when referee Tony Harrington pointed to the spot in United's area but Bournemouth's hopes of snatching a late, late win were dashed when a lengthy VAR check downgraded it to an indirect free-kick just outside the box.
Erik ten Hag's side went into the game in seventh place, after dropping below Newcastle United - 4-0 victors over fifth-placed Tottenham Hotspur in the lunchtime kick-off - and remained there after being unable to complete the comeback with another winning goal.