After claiming just one point from six matches in charge since replacing Alan Archibald in October, goals from Blair Spittal and Miles Storey ended the agony to pull Partick off the foot of the table.
However, nothing is ever straight-forward at Firhill and Dunfermline are not convinced that Storey’s clinching goal was over the line.
Caldwell said: “We’ll take the decision [for Storey’s goal]. Miles has pace and when he wants to run behind defenders he must be difficult to play against.
“I’m delighted for everyone at the club. It’s been a long time coming but we got what we deserved.
“It’s a start and we have to put a run of results together. With that desire and commitment, I’m sure we can do that.”
Thistle were ahead in 12 minutes and it was fitting that the game’s best player was on the score sheet.
James Penrice, who also had a fine match, crossed from the left, Kris Doolan won the aerial battle to knock it down to the edge of the box and Spittal drove a terrific shot into the left corner.
Lee Robinson made a fine save to deny Storey in 21 minutes, Andrea Mbuyi-Mutombo should have scored but headed over the bar and Robinson then denied Doolan in 31 minutes, assessing the situation quickly to make a fine block after Dan Jefferies, making his Thistle debut, played the ball forward.
Suddenly the Pars came to life just before half-time but, crucially, Thistle survived.
Robbie Muirhead hit the top of the bar with a ferocious left-foot shot in 39 minutes then Danny Devine’s downward header bounced up to hit the bar in 43 minutes before Jamie Sneddon clawed it away.
In first-half injury time Sneddon superbly pushed Faisal El Bakhtaoui’s header over the top after Ryan Williamson crossed from the right.
Partick then sealed the victory they craved 11 minutes into the second half. Penrice took a pass from Christie Elliott and brilliantly burst into the box to set up Storey, who sent a clever back heel towards the left corner. Robinson desperately tried to claw the ball out but assistant Alan Grainger flagged that the ball was over the line.
Dunfermline manager Allan Johnston said: “It was a big call for the second goal which was the sucker blow. It’s impossible for the linesman to see if the ball’s in or not with the way Lee dives. I don’t know how the linesman can give that.
“Usually players are honest, but they were adamant that it hadn’t gone over. It was very close but they’re probably the defining moments that kill you.”