United's first group game in the Leasing.com Trophy was the home match against the under-21 side from Wolverhampton Wanderers.
Boss Steven Pressley made eight changes to the starting line-up from Saturday with Christie Elliott, Jarrad Branthwaite, Louis Gray, Jon Mellish, Canice Carroll, Elias Sorensen, Ryan Loft and Hallam Hope all given the nod to make the step up.
Louis Gray and Jarrad Branthwaite made their senior debuts for the club, and striker Hallam Hope was handed the captain's armband.
United earned a corner within the first minute but a high, looping delivery from Bridge brought a whistle from the referee as he judged that keeper Andreas Sondergaard had been impeded.
The ball spent long periods in the middle areas of the pitch as both sides tried to pass it around through the tight early stages, but Hallam Hope raised a ripple of applause when he put his head down and set off on a run which took him up against the heart of the defence. A powerful shot from 20-yards took a deflection and bounced wide of the upright.
A long throw from Iredale followed, and he found Sorensen inside the area, but his flicked header dropped onto the roof of the net.
More good work down the left flank saw Mellish combine with Iredale and a driven cross brought a run across the face of goal from Loft. His touch hit a defender and that made the save easy for Sondergaard to make.
A run and drop of the shoulder from Elliott opened a gap to shoot, as the game kept up a fast pace, but his toe poke was met on the dive by the keeper. Wolves broke quickly with a lovely through ball from Samuels, which released Benny Ashley-Seal, and he made no mistake as he slotted a clipped effort past Gray and into the back of the net.
The Blues had plenty of the ball, both before and after the goal, but Wolves defended the crosses well with some timely interventions and clearances.
Striker Ryan Loft sent a header and then a long-range volley over the bar as he tried to make things happen, and a surge from Bridge took him into a dangerous area. Hope took over, with a first time shot, but it crashed into a defender and the moment was gone.
United thought they'd done the job on 30 minutes when an intelligent pass from Loft put Sorensen beyond the back line. A low delivery hit an outstretched leg and that was enough to take it beyond the slide of Hallam Hope as he arrived late at the far post.
Wolves broke again as they regrouped and Ashley-Seal stayed wide as he waited for the ball to come his way. His shot hit Jones and Gray was relieved to see it spin past his upright as it completely changed course.
Carlisle were back on terms when Elliott picked the lock with a superb ball forward. Hope timed his run perfectly and he did everything right as he guided it over the advancing Sondergaard and over the line to register his first goal of the season.
The Wolves stopper came out on top of the next contest between the pair when he got down sharply to deal with a grasscutter from the lively Blues forward.
And the visitors were back in front on 39 minutes when Tsun Dai took matters into his own hands as he angled a run in from wide. His shot took a wicked deflection off Carroll and Gray had no chance as it whipped into the Warwick Road End target.
United were close to pulling level almost straight away when a half clearance from a Bridge corner fell invitingly in front of Loft. He tried to lob it into the top corner but he got his bearings wrong and it fell agonisingly wide.
But the hosts got their second goal on the stroke of half time as Bridge and Sorensen combined to carve their way through the visiting defence. Loft checked his run before picking his spot with Sondergaard left to flap at thin air.
United found themselves behind again within two minutes of kick off in the second half when an underhit backpass from Branthwaite was pounced upon by Ashley-Seal. Gray charged off his line and referee Seb Stockbridge had no hesitation in pointing to the spot as the forward tumbled to the floor. He dusted himself down before rattling an unstoppable penalty into the roof of the nets.
Carlisle sent men forward and Sorensen bullied his way into the box with a determined run. The ball eventually came to Hope but Sondergaard arrived at the same time and his attempted clearance ricocheted off the striker and crept away to safety.
Chances continued to come at both ends and a misplaced pass in midfield from the away side had Loft very interested, but his shot from distance was too close to Sondergaard.
Substitute Aaron Hayden wasn't too far away as he jumped high to meet a whipped corner delivery. The connection was good but it was just a yard too high.
An already difficult task became a real test for the hosts when a fantastic through ball left the unmarked Oskar Buur with time on his hands and acres of space to work in. His cut back was met on the full by the predatory Benny Ashley-Seal and Gray could do nothing as his hat-trick effort whisked past his dive.
A shot from the edge of the area from Sorensen was once more too close to Sondergaard as the Blues looked to recover from their second half setbacks, but they couldn't get their passing game going in the opposition half and it becamse a frustrating spectacle as move after move broke down.
Harry McKirdy marked his introduction with a trademark weaving run, but his snapshot was high when Hope fed the ball back into his path.
The trickery shown by McKirdy caused problems for the Wolves defence and another good move gave Sorensen another half chance. He pulled the trigger early but he was quickly charged down. Hayden's header from the resulting Bridge corner was also blocked at source.
Mellish and Iredale tried their luck as the clock ticked down, and Hope headed wide from an Iredale cross. It it just wouldn't fall for the Cumbrians and it was the young Wolves side which celebrated the victory come full time.
Carlisle United - Hope (35), Loft (45)
Wolverhampton Wanderers U21 - Ashley-Seal (20 & 47 pen, 64), Dai (39)
Carlisle United - Carroll (52)
Wolverhampton Wandereres U21 - Hanne (90)
Carlisle United - Gray (gk), Branthwaite, G Jones (Hayden 60), Mellish, Elliott, Carroll, Bridge, Iredale, Sorensen, Loft (McKirdy 77), Hope. Subs - Collin (gk), Barnes, Charters, Kerr, Olomola.
Wolverhampton Wanderers U21 - Sondergaard (gk), Taylor (c) (Hanne 70), Nya, Thompson, Ashley-Seal (He 81), Samuels, Buur, Dai (Otasowie 85), Cristovao, Watt, Richards. Subs - Pardington (gk), Wan, Csoka, Marques.
Referee - Sebastian Stockbridge
Assistant Referee 1 - Paul Newhouse
Assistant Referee 2 - Barry Gordon
Fourth Official - Paul Brown
Attendance - 893 (72 away fans)