The AFC Wimbledon loanee played a starring role down the right flank, bringing the Bantams faithful to their feet with some exhilarating wing play and running rings around visiting left-back Jack Iredale.
And that enjoyment factor is a two-way street, man-of-the-match Connolly revealing that he he had a ball in what was by some way City’s most potent performance since relegation from League One.
“I enjoyed it a lot out there,” the Irishman said. “I felt really strong and really fit. I think that’s my fourth game in a row and I can feel myself getting stronger, so I enjoy the game more and get involved more and make things happen. I feel very close to being 100 per cent now.
“I felt like I was getting a lot of the ball and that’s down to the lads feeding out. When you’ve got direct wingers in your team it’s their job to get you up the pitch and run at the full-backs, try and create things. If I wasn’t doing that I wouldn’t be doing my job.
“I’m loving it here, so long may it continue.”
Bantams boss Gary Bowyer said: “He was a constant threat straight away. His pace gets people off their seats.
“He’s growing with confidence every game, every minute that he gets into his body fitness-wise.
“Being greedy, I just need one or two better end products from him and he knows that himself. He wants to contribute more goals and assists.”
For all Connolly’s fine work, it was City’s other winger, Harry Pritchard, who made the first telling impression on the match from a Bradford perspective, drawing his team level on the half-hour-mark after Olufela Olomola handed the Cumbrians a 14th-minute lead when he beat Richard O’Donnell with a neat finish from a narrow angle.
Prior to their equaliser, City had struggled to create anything going forward, but just as the home faithful began to show signs of frustration, a breakthrough arrived.
Pritchard managed to hold off a couple of defenders inside the United box and fire left-footed across Adam Collin and into the far corner of the net.
With both the game and the atmosphere inside the stadium transformed, Carlisle’s Jack Bridge was then sent off for a second bookable offence.
City took the lead when some Connolly magic earned a free-kick and Palmer delivered from the right for Kelvin Mellor to nod in at the back stick.
A third and decisive ‘goal’ appeared to have arrived just six minutes after the resumption.
Connor Wood curled over a cross from the left that captain James Vaughan headed straight at Collin before Clayton Donaldson forced the ball over the line.
The home celebrations were in full-swing as referee John Busby initially appeared to have awarded a goal, only for the strike to eventually be ruled out for handball.
Undeterred, Bowyer’s men kept coming and Vaughan met Connolly’s low right-wing cross and forced Collin into a fine stop at his near post, Donaldson stabbing the rebound against the woodwork. Seconds later, the referee evened things up, Ben Richards-Everton shown a straight red card following a 62nd-minute lunge on Iredale in midfield.
Bradford continued to look the more likely despite this setback, Cooke doing superbly to intercept then play Connolly through on goal, only for the Irishman to scuff his finish.
Cooke then shot narrowly over the bar himself, while Nathan Thomas was just wide at the other end as Carlisle pushed for a way back into the game late on.
However, in stoppage-time City finally made the points safe.
With the Cumbrians having committed men forward, Donaldson was able to break and send a pass from left to right across the edge of the box for substitute Zeli Ismail, who produced a couple of step-overs and then lashed a strike into the roof of the net.
Bradford: O’Donnell, Mellor, P O’Connor, Richards-Everton, Wood, Connolly (Ismail 78), Palmer, Cooke, Pritchard (Oteh 82), Donaldson, Vaughan (A O’Connor 71). Unused substitutes: Hornby, McCartan, Henley, Devine.
Carlisle: Collin, Sagaf (Sorensen 82), G Jones, Webster, Knight-Percival, Iredale (Hope 73), Bridge, M Jones, McKirdy (Elliot 38), Thomas, Olomola. Unused substitutes: Mellish, Gray, Branthwaite, Loft.
Referee: J Busby (Oxfordshire).