United produced yet another strong performance with their first away win of the season as their impressive unbeaten start to the campaign continues.
The sides exchanged early set pieces in the blistering heat but keepers came out on top as they closely watched the balls into their box.
A deep delivery from Grainger brought half an opening for Adams, as it fell out of the sky from a headed clearance, but he couldn't get over the volley and he sent it high over the bar.
Tom Miller stretched the back line with a long throw as Carlisle dominated territory and a poor kick from N'Gala set Joyce up for the shot. He connected well but the big defender recovered to make a block.
Good approach play down the left flank saw Grainger and Adams combine to win a corner and the delivery from Adams found Raynes on the run. He got a leg to it and Stephens was relieved to see it bounce down off the underside of the bar. Lambe recovered the clearance and he spotted Devitt in acres of space. The wide man opened his body and was a whisker away from bagging the first goal of the day when he bent a low effort just past the upright.
It was Carlisle who looked the most likely and they deservedly took the lead midway through the half when Gillesphey popped a long ball at Nicky Adams. He controlled it beautifully and his whipped cross left Jabo Ibehre with the happy task of crunching it into the back of the net to register his first goal of the campaign.
United went close again when another Adams cross found Ibehre shoulder to shoulder with N'Gala. A ricochet took it clear but it was a brief respite as Jones put Adams into another good area. He went for an early cross and Stephens had to move quickly to flick the dipper over the angle of post and bar.
The left flank approach proved to be a fruitful avenue once again when Grainger put Adams behind the back line of defence. He had options in the middle but he went for glory and was disappointed to see it bend just wide at the last moment.
Carlisle should have doubled the lead just ahead of the break when Jones put Devitt past his man on the right. A first time cross brought a leap from Ibehre but celebrations turned to disappointment as it went just past the angle of post and bar.
A 23-yard Grainger free kick was deflected wide as Carlisle started the second half on the front foot and a wonderful move needed a block from N'Gala when Adams, Devitt and Raynes worked it to Lambe 17 yards out. His shot was going in until a boot got in the way.
Jamie Devitt was next to test the stopper when he carried the ball from deep. The lack of a challenge invited the shot but Stephens dropped low to gather.
Captain Danny Grainger was the width of a blade of grass away from putting one away with his right foot when the ball was worked wide from Joyce, via Jones, to the unwatched left hand side of the pitch. A determined run preceded the shot and Stephens was pleased to see it bounce past his net.
The missed Carlisle chances were almost punished when substitute Vilhete cut the ball back to the penalty spot at the other end. Akinde prodded at it but Raynes and Miller were locked together to make a block. Batt tried to pounce but brave defending preserved the clean sheet.
Lambe smashed a delivery on the run onto the outside of the post as the game opened up, but Barnet started to have more of a say and Gillespie had to be watchful as a shot from Batt flew through bodies.
Shaun Brisley came on to make his first appearance for the club with just over 15 minutes to play and the switch helped to shore things up and slow the home momentum down.
A 30-yard Nicky Adams free kick hit the wall and dropped over the bar as United worked hard to keep the upper hand, but Gillespie had to stay big to save with his foot from an Akinde drive as Barnet increased the tempo.
But game management and determination saw the job through as the Bees lobbed ball after ball into the box, only to be thwarted by more excellent defending.
Carlisle United - Ibehre (21)
Barnet - Nelson (76)
Carlisle United - Ibehre (33)
Barnet - Stephens, Johnson, N'Gala, Nelson, Watson (Batt 46), Weston, Akinde, Togwell, Taylor, Akpa Akpro (Gambin 60), Nicholls (Vilhete 55). Subs - Vickers, Sesay, Muggleton.
Carlisle United - Gillespie, T Miller, Raynes, Gillesphey, Grainger, Lambe, Jones, Joyce, Adams (Penn 84), Devitt (Wyke 63), Ibehre (Brisley 74). Subs - Crocombe, Ellis, McKee, S Miller.
Referee - Mr Robert Jones
Attendance - 1,620 (298 away fans)