Rooney had been a player-manager of the club since the end of November but was appointed the manager of the club on Friday and with a win against a side fighting for promotion to the Premier League, it has temporarily moved the Rams two points clear of the drop zone.
Meanwhile, for Jason Tindall and his side, this result marks a second consecutive 1-0 defeat and it moved them down to fifth in the Championship table following Reading's 3-0 victory over Coventry City.
Story of the match
The hosts made a bright start as could have broken the deadlock inside three minutes when a cross from the left by Bielik was met by Kamil Jozwiak at the back post but his downward header was clawed away to safety by Asmir Begovic.
Six minutes later Bournemouth had a golden opportunity to net themselves when Jack Stacey was found in space down the right-hand side and his low cross found Dominc Solanke unmarked inside the area, but from point-blank range he somehow was unable to convert past Kelle Roos.
Despite Bournemouth dominating possession just after the half an hour mark, Lewis Buchanan had a great chance to hand the Rams the lead when he was slipped in one-on-one by Bielik, but his low shot was blocked well by the feet of Begovic.
However, only a minute later Derby did take a deserved lead when from a corner Bielik reacted first to a loose ball inside the area and he found the composure to poke the ball into the back of the net.
After the deadlock was broken Rooney's side started to control the game and Jason Knight had a sighter after finding space from range, but his swirling shot sailed well off target.
At the break, the Cherries made a double change and almost immediately were level when one of their changes Joshua King got on the end of an Arnaut Danjuma cross but his header was straight at Roos.
Bournemouth decent start to the half continued when Solanke latched on to a long ball but his half volley from a tight angle could only find the side netting.
Two minutes later down the other end full-back Nathan Byrne was picked out in space but his well-hit strike from range landed straight into the chest of Begovic.
With 20 minutes remaining, Bielik nearly grabbed a brace when he latched on to a loose ball on the edge of the box, but his low goalbound shot was impressively blocked by Chris Mepham.
Nine minutes later Roos made a superb save to keep Derby ahead when a Solanke header from close range was magnificently parried away to safety by the 28-year old.
Then, when the away side were really piling on the pressure with three minutes remaining, Stacey was agonisingly close to rescuing a point, but his low strike from the edge of the box flashed just wide of the left-hand post in what ultimately proved to just not be the Cherries' day.
Cherries lacklustre first half display costs them
In the first period, despite Solanke missing a gilt-edged opportunity the visitors never seemed to get going as they really struggled to get in behind and cause Derby's back three any serious issues.
This is something that ultimately they would end up rueing as it meant going into the second half they were always chasing the game.
Then despite creating some decent opportunities in the final 45 minutes, the best of which fell to Solanke with 11 minutes remaining Tindall's side did not really do enough to grant them of walking away from Pride Park with a point.
Dogged defensive performance sign of things to come
The result for Derby is not the only thing that Rooney will be pleased with tonight, he will further be happy with how this result marks the team's first clean sheet in five games.
The Manchester United and England legend opted to go with a three at the back formation and even when they were put under pressure in the last 15 minutes, the Rams did fantastically well to deal with the long balls delivered into the box and to limit the Cherries to few opportunities
This is something that Rooney will be particularly satisfied with and now he will want to build on this defensive showing in games going forward.
Stand out player- Krystian Bielik
The midfielder who joined Derby from Arsenal back in August 2019 not only bagged the goal that earned his side all three points, but he looked very composed and controlled the midfield battle throughout the entirety of the game.
The 23-year-old did not allow Bournemouth's midfield to pass through him on many occasions at all and when space opened up in the final third, he played key passes in behind the visitor's defence which consequently helped cause a danger and threat on the attack for the home side.