United have struggled for consistency all season but the victory 3-0 win against lowly Watford at Old Trafford lifts them to 41 points, just three behind fourth-placed Chelsea.
Midfielder Fernandes, bought by Solskjaer last month to add creativity and drive to United's midfield, scored from the penalty spot shortly before half-time and Anthony Martial and Mason Greenwood also found the net.
"This is what I want to do and what I need to do," Fernandes told the BBC.
"Everyone knows we want to get into the Champions League places. I am here to help the team conquer this place and keep winning games."
Solskjaer said he wanted his side to "kick on" after two consecutive wins and clean sheets.