Callum Cooke's second-half curling free kick wasn't enough to peg back a youthful Nottingham Forest side who dealt two hammer blows five minutes before the interval. Watford loanee Philip Zinckernagel and Carvalho combined for both goals and rewarded Forest for their assured first round showing.
Story of the match
Bradford started the evening in the ascendancy, with Cooke crafting the opening chance of the tie. After a bright passing move, Cooke found himself in space inside the hosts 18-yard area, but his glancing header was comfortably claimed by debutant Ethan Horvath.
After a slow opening five minutes, Forest grew into the game, with the tempo of their play increasing as they began to pressurise Bradford in the final third.
Fin Back was the first to connect with a Zinckernagel corner, but his effort sailed wide of the post. Alex Mighten's tricky feet on the left flank opened up another opportunity for the Reds minutes later, but his low driven ball across the box fell to Zinckernagel, who lost his footing and squandered the opportunity from close range.
On 25 minutes, Horvath was called into action when Lee Angol arrowed a shot towards goal from range. After a neat flick over the head of Back, Angol shaped up the shot and tested the American stopper - who was alert to palm away the powerful effort from danger.
Shouts for a Forest penalty were waved away just before the half-hour mark by referee Peter Wright, and it denied what would've been a superb mazy solo run from Mighten, after some beautiful footwork to deceive three Bantams defenders.
Bradford had to throw bodies in front of Mighten's close range strike as the hosts continued to crank up the pressure. Some neat work between Carvalho and Zinckernagel set Back free in acres of space on the right side, and he found Mighten but the Bantams threw a sea of white shirts in the way of the ball.
The Reds were rewarded for their dominance, not once but twice, in an unrelenting five minutes that saw them put the Bantams to the sword and head into the interval 2-0 up.
A brilliant move started by Tyrese Fornah, who shone brightly in the first-half, found its way to Zinckernagel who drilled the ball across the area for Carvalho to convert from close range, for his first goal since returning from last campaign's loan spell at UD Almeria.
The pair combined once more moments later, as Forest doubled their advantage through Carvalho again. The Watford loanee picked out Carvalho after another fast tempo passing move from the Reds, and he calmly slotted the ball low past Richard O'Donnell.
The opening of the second-half saw two quick fire chances, with Forest’s stopper first getting low to deny Angol once again from close range, before Jayden Richardson darted down the left on a lengthy run and fired into the side netting.
Cooke halved the deficit shortly after the interval though, with a beautiful free kick. It served as an inviting opportunity for the Bantams, and they snatched it with both hands. Cooke curled his effort superbly round the Forest wall and past a sprawling Horvath.
Carvalho had a superb chance to grab his first hat-trick in Forest colours, but was denied by O'Donnell. Richardson's initial strike was a powerful one from outside of the area, and the block sliced into the path of Carvalho but the Bantams stopper made a smart reflex stop.
The visitors threatened Forest with a couple of late chances, but it wasn't anything venomous enough to test Horvath who stood firm in the Reds net.
Inspiring display from Carvalho
On his return to the City Ground, Carvalho shone and now leaves a big question as to whether he will be considered to start Forest's second game of the Sky Bet Championship season on Saturday against AFC Bournemouth.
Carvalho twice combined with new arrival Zinckernagel, and was a bright spark all evening, as he combined with Forest's academy graduates surrounding him to transition play from the midfield to attack.
Forest fans are aware of the quality the Portuguese attacking midfielder possesses, and with a string of games, once again could help rediscover the form of their record signing. He can certainly take confidence from tonight's display.
Youth can play an important role this campaign
They commanded respect from the supporters and performed in an experienced manner for such a young group.
The back four was scattered with four debutants, but they held their shape well and looked assured in the first half before more experienced heads joined the fray.
With a much smaller squad than previous campaigns, Forest may call upon some youthful options this season to fill the gaps of injury or absence.
Tonight's performance coupled with minutes over pre-season, is a great building block for these youngsters to progress and get more game time at Forest.
Man of the match
Although Forest can take a lot of promising factors out of Carvalho and Zinckernagel's performances, it was a stellar showing all evening from youngster Fornah.
From the opening whistle he controlled the midfield, looking patient and calm in possession, whilst receiving and offloading the ball positively into attacking wide positions.
His range of passing, vision and tackling rounded off a complete midfield performance by the 21-year-old, which impressed the supporters and surely manager Hughton.