Lukas Jutkiewicz capitalised on a mix up between Yann Kermorgant and Charlton goalkeeper Ben Hamer to score the winner 18 minutes from time.
Defeat to Leicester in the league opener and Accrington Stanley in the Capital One Cup in midweek had increased the pressure on Mowbray's side.
But now the Boro boss is hoping Jutkiewicz's strike can kick-start an unbeaten run.
"Managers live and die by their results so it was important for us to get the win," he said.
"We controlled the game for long spells but we've just got to make sure we put the ball in the net more often because it could easily have gone the other way today.
"We've been letting ourselves down in both boxes in our opening two matches and we put in a much better display. Now we have to try to build some momentum from this and move forward."
Charlton were second best from the start and it took them until first-half injury time to muster a shot.
They came close to taking the lead through Danny Green before Boro's winner but the Londoners find themselves still without a point after two league matches.
And manager Chris Powell admitted they have to improve their level of performance quickly.
"Sometimes there's games when you just have to accept it's not going to flow the way you want and it wasn't to be today," he said.
"We didn't have that spark that I expected from our first home match of the season.
"The goal summed up our day - Yann's normally great in both boxes but he just didn't get enough on his header and it fell to their striker.
"We had one or two incidents but not enough for me. We've got to be a bit more streetwise but just one result can turn it around in this division."
Middlesbrough have tabled a bid for Leeds striker Ross McCormack as Mowbray attempts to strengthen his squad before the transfer window shuts on September 2.
Winger Albert Adomah made his debut having signed for £1million from Bristol City this week but the Boro boss believes they still need more quality to mount a serious promotion bid.
He said: "We're trying very hard to add quality to our squad because we lost 11 players at the end of last season but only replaced them with four. We've got bids in with two or three clubs at the moment and hopefully we can do a deal to help improve the squad in the next week or two."