Carlisle made the first opening, following a tight start, when Joyce threaded the ball through from midfield. Hope took it on his chest and he twisted and wriggled before he forced a near post save out of Stephens.
More good football followed from United and a neat touch from Wyke put Hope clean through. Stephens sprinted out to make a vital block.
Barnet had a good spell on the quarter hour but consecutive corners brought nothing as the away defence held strong.
Front man Jabo Ibehre was gifted a chance when N'Gala lost control of the ball 30 yards out, with United looking to get forward at every opportunity. A touch from the striker preceded a shot which Stephens was able to hold.
Barnet finally showed as a dangerous force on 20 minutes when a long ball took Gambin wide. His cross was perfect for Hoyte but the right back was out of his depth and he could only stab a poor volley high into the stands. It was better from the Bees and another high ball found Carlisle light at the back. Batt sneaked in but his run lacked conviction and he screwed his shot on the run well wide.
It was suddenly end-to-end and Hope did well to beat a sliding tackle as he angled for the edge of the area. He struck it well but Stephens was relatively untroubled. A poor kick out from the stopper brought more pressure and Kennedy was a whisker away with a crunching volley which dipped an inch past the upright.
Barnet came again on 20 minutes with a long ball which sent Gambin wide. His cross was a good one but Hoyte lacked confidence and he could only stab a weak volley high into the stands. It was better from the hosts and another high ball found Carlisle light in numbers at the back. Batt ran onto it but his shot lacked conviction and he screwed it wide as Gillespie bore down.
The game opened up and Hope did well to beat a sliding tackle as he angled for the edge of the area. He struck it well but Stephens was able to pull it in. A poor kick from the stopper brought more pressure and Kennedy went close with a crunching volley which dipped an inch past the upright.
A Grainger corner found Kennedy unmarked at the back post as United pushed on and his return cross was volleyed instinctively by Hope. Stephens had to scramble to tip it over the angle of post and bar.
Both sides plugged the gaps ahead of the break and a long range shot from Grainger spun past the post as he tried to make things happen. Wyke was next to go on a run but his low cross bounced awkwardly and Hope sent a half volley over the target.
Gash had a shot at the other end which deflected into Gillespie's hands, but it was honours even at the break with everything still to play for.
A screwed shot off the laces from Batt signaled the start of the second half action, and Barnet went close again when Gambin put the ball in from a one-two with Batt. Dembele was up high but his firm header flew just over.
Carlisle responded with a good chance of their own when a long ball put Wyke one-on-one with Stephens. He went for power but he couldn't keep it down.
Gambin started to look a threat and his jinking run and cross had Batt interested. Another weak header made things easy for Gillespie between the sticks. The nippy midfielder took matters into his own hands when Barnet came forward again, but his 25-yard curler was watched all the way by the United stopper.
Grainger did well to send a cross into the mix as he came under pressure on the left flank, when United regained the upper hand, and a touch from Wyke was just too heavy as Kennedy arrived late at the far post.
Wyke rattled a training ground corner routine over the bar when Grainger fooled Barnet with a low delivery, and the busy forward was unlucky again when his thumped shot was blocked as it headed for the bottom corner in Carlisle's next attack.
A fantastic piece of skill from Hope was worthy of note as he somehow controlled a wayward pass with his heel as United stayed on the front foot. His second touch took him through two sliding challenges and his third was an accurate punt which Stephens had to deal with.
Carlisle had the bulk of the possession through the closing stages but a blocked Grainger shot and a looping Raynes header were dealt with by the Bees, and it was honours even at the end of what had been a tight game.
Barnet - N'Gala (19), Hackett (25), Sesay (90)
United - Joyce (9)
Barnet - Stephens, Hoyte, Johnson, Dembele, N'Gala, Weston (Randall 76), Gambin, Togwell, Gash (Champion 58), Batt, Hackett (Sesay 58). Subs - McKenzie-Lyle, Muggleton, Nwogu, Taylor.
Carlisle United - Gillespie, Atkinson, Ellis, Raynes, Grainger, Hope (Gilliead 72), Joyce, Hery (Sweeney 82), Kennedy, Wyke, Ibehre (Asamoah 89). Subs - Hanford, Miller, Dicker, Archibald-Henville.
Referee - Mr Stephen Martin
Attendance - 2,079 (559 away fans)