Goals by Marcus Rashford and Anthony Martial - Abdoulaye Doucoure getting a late goal for the visitors - took them above Arsenal and level on points with third-placed Tottenham, who play at Liverpool on Sunday, boosting Solskjaer hopes of achieving his first goal of securing Champions League football for next season.
It was not vintage United as Watford had more shots on target and more corners than their hosts, but it was much needed after successive defeats against Arsenal in the Premier League and Wolves in the FA Cup.
But it was a good reminder, if one was needed for the new permanent manager, that there is plenty of hard work ahead if Solskjaer wants to make United contenders for the title again.
His record over the 19 games in interim charge, and how he has lifted the mood around the club, had made his appointment as Jose Mourinho's successor a foregone conclusion.
The Stretford End was in no doubt about their former hero getting the job as a giant banner was unfurled as he emerged from the tunnel before he could take his position in the dugout.
But it was the visitors who started the brighter as Doucoure dragged a shot wide from a promising position while David de Gea had to claw away a header from Troy Deeney.
Watford have an FA Cup semi-final on the horizon against Wolves next Sunday and a place at Wembley must have given the players a spring in their step as De Gea had to deal with further efforts from Roberto Pereyra and Gerard Deulofeu.
But it was their desire to go forward which proved their undoing as they were caught out by one of the counter-attacks that Manchester United have specialised in down the years.
Deeney failed to get his pass beyond Luke Shaw and the left-back sped forward, before looking up and playing a perfect ball into the space behind the defence for Rashford to sprint onto and coolly finish past the onrushing Ben Foster.
It was the ninth goal during Solskjaer's reign for Rashford, who has blossomed in the last three months, and has replaced Romelu Lukaku as United's main man up front.
Foster, once of United, has been Watford's best player this season, and he underlined why with a brilliant instinctive save to deny Martial from close range as United threatened to take control.
Rashford was at the heart of their attacking play as he rounded Foster but from a tight angle could not find a team-mate.
Watford continued to push forward after the break in search of an equaliser and Pereyra's goalbound effort was pushed behind by De Gea, while Will Hughes curled another shot beyond the far post.
It was no surprise to see Solskjaer respond with a double change as Andreas Pereira and Jesse Lingard were sent on and it worked a treat as the pair combined to tee up Martial, who scored from close range at the second attempt.
Watford kept pressing and Doucoure scored in the 90th minute as he showed fabulous footwork inside the area to make things nervous, but it was a little, too late to ruin Solskjaer's day.