The Boro boss had been under mounting pressure after a string of draws left his side languishing in the lower reaches but was upbeat after a vital victory.
Boro were caught cold at the back as Andy Williams raced through to put Yeovil ahead after four minutes.
But they levelled quickly through Grant Leadbitter and Albert Adomah stabbed them ahead before the break after Leadbitter's penalty was saved.
A second-half strike from Jacob Butterfield and a Kei Kamara header wrapped up a polished win.
"We gifted them an early goal but the reaction to that was very positive," said the Boro boss.
"We got the equaliser very quickly, we went ahead, we hit the bar, we hit the post, and we got ahead and stayed composed. It was a good display.
"So is it a relief? I don't think so. We have been playing well in recent weeks and we knew it would come.
"But yes, it is important to turn those good performances into wins. Six draws from 11 games is too many and all of those felt like defeats to us because we probably warranted more than a single point in all of those.
"We have never lacked confidence. We have played some very good football over the season."
But Mowbray admitted that the team was still far from the finished product and are leaking too many costly goals.
"We know we maybe need to add some more quality at the back and cut out the individual mistakes that are leading to goals against us," he said.
"We've only had one clean sheet all season and that's not enough if we are to get out of this league so that is something we have to work on over the next few weeks."