Carlisle started in confident mood and Jones and Adams set the tone as they battled for every ball in midfield. The pair combined well on the right flank to rob possession and Lambe came across to help out as the home side edged forward. Adams showed again on the edge of the area but his clipped cross was just too high for Shaun Miller to convert.
Cheltenham had a brief sight of goal when a long ball forward fell nicely for Waters but he was off balance as he screwed a wild shot into the stands.
The Blues regrouped and forged a path down the right hand side as Adams and Tom Miller worked off each other tight by the touchline. An early delivery had to be cleared as Wyke and Miller waited in space.
It was all about the hosts and Wyke did well with his back to goal when he shielded the ball before twisting to complete a cross. Shaun Miller nodded it back across the face of goal and Parslow had to guide it behind as Lambe raced in to try to finish it off.
A slick and rehearsed corner routine caught the Robins napping when Grainger sprinted in to meet a low pass. A thumping left foot drive had goal written all over it until Griffiths got fingers to it to tip it onto the bar.
Carlisle kept the pressure on and blocked shots from Adams, Tom Miller and Wyke reminded the visiting back four that they were in for a busy night.
Cheltenham struggled to get out of their own half but the lively Billy Waters led a rare foray forward as he tried to provide a much needed outlet. In the end his only option was a long range shot but it was never going to trouble the target.
All that was missing for the hosts was a goal and they went close again when Wyke chested a high ball down for Adams to pounce. His shot went through legs but Griffiths reacted well, despite seeing it late.
The Cumbrians were a whisker away from opening the scoring on the half hour when team captain Danny Grainger took charge of a 28-yard free kick. He hit it on the sweet spot but he was frustrated to see it dip and bend its way just past the angle of post and bar.
More frustration followed when Joyce, Lambe and Adams linked up to put Shaun Miller into a good area. His first touch took him away from his man and his second left Griffiths for dead as a cheeky chip dropped over the keeper's head. The crowd readied itself to celebrate until the ball crashed against the upright and ricocheted away to safety.
Luke Joyce rattled a long range effort wide as the chances kept coming and more heroics from Griffiths prevented Wyke from popping a perfect Grainger cross into the top corner. The keeper was at full stretch to make the save.
It was groans all round from the resulting corner as Raynes stole the run on his marker to get to the ball first. A firm header flashed across the goal and an inch past the target.
A piercing cross from Tom Miller had Wyke on his toes once more at the start of the second half and Griffiths did enough to readjust and palm it over the bar. The Robins broke from the corner and they had Carlisle worried as a low cross skipped behind the back line. Wright was unmarked but he couldn't find a touch.
Charlie Wyke typified the United approach when he took the ball off Pell on the halfway line. A surging run followed and it needed a tackle from Parslow to stop him from going clean through.
Having almost completely dominated Carlisle were dealt a cruel blow when they over committed in search of the elusive goal. Cheltenham broke the attack down and raced forward with men to spare. A lovely pass left Harry Pell with the simple task of slotting the ball into the bottom corner.
Substitute Jabo Ibehre used his presence to cause problems from the moment he entered the fray and he grazed the top of the bar with a wicked header which had Griffiths flapping at thin air.
Danny Wright swept a 24-yarder high after he had taken the ball down with a lovely touch, but it was Carlisle who pushed forward with intent as they peppered the box with crosses from wide.
Billy Waters was booked for simulation when he took a dive when he nicked the ball past Gillespie, and the United keeper was in action again when he dropped late to parry a stinging Pell free kick as it went under his wall.
Carlisle settled into their stride again late in the day and a dipper from Adams was cleared behind by Cranston as it dropped onto his line. Grainger recovered the half cleared corner and Kennedy registered the third home strike against the woodwork of the game when he clipped it onto the underside of the bar.
Another break from Cheltenham left Cranston with room to cross as the clock ticked down but the hosts finally got some reward when a ball into the box found Kennedy with the target in his sights. He pushed and bustled and got the touch it needed to send it over the line.
Devitt could have capped off a great finish to proceedings when he controlled a punch from Griffiths 16-yards out. He tried to lob it into the top corner but he put too much on it and it went an inch over the bar.
Carlisle United - Kennedy (90)
Cheltenham Town - Pell (57)
Carlisle United - Grainger (71), Waters (72), Pell (85)
Cheltenham Town - Suliman (63)
Carlisle United - Gillespie, T Miller, Raynes, Ellis (Kennedy 73), Grainger, Lambe (Devitt 58), Joyce, Jones, Adams, Wyke, S Miller (Ibehre 59). Subs - Crocombe, Atkinson, Gillesphey, Penn.
Cheltenham Town - Griffiths, Barthram (Dayton 46), Parslow, Pell (Rowe 88), Waters, Wright, Hall, Cranston, Whitehead, O'Shaughnessy, Suliman. Subs - Jennings, Kitscha, Lymm.
Referee - Mr Michael Salisbury
Attendance - 4,203 (117 away fans)