The club captain saw his effort hit the back of the net thanks to a deflection to ensure replay, however, on another day the talisman could have had a hat-trick.
Defender James Butler had the first chance of the game on 20 minutes when he got on to the end of Lee Williamson's free-kick. However, his header hit the side netting.
Malbon should have opened the scoring on 30 minutes when he beat Harry Pickering with his effort. However, a recovering defender cleared the shot off the line. The ball fell to Williamson who saw his shot blocked.
It was all Kidsgrove in the first half as Williamson had a volley that went just wide of the goal, while Malbon headed another effort wide.
Cole almost scored against the run of play on 43 minutes, when a ball was played over the top to him and, he spotted Keiran Harrison off his line. He tried an effort which thankfully for the Grove, the ball hit the bar and bounced out of play.
The visitors took the lead just four minutes into the second half when a cross found James Askey who was found unmarked in the area. The defender made no mistake to head home the opening goal of the game.
It allowed the visitors to get on the front foot as right-back James Melhado got forward and saw his shot parried away by Harrison. While the keeper had to save a shot with his leg from Serkari Ahmadi to keep it at 1-0.
From there Kidsgrove laid siege to the Castle goal looking for an equaliser. Kyle Blake and James Jennings got in each other's way as they went for the same ball. Jennings also had a shot that went over the bar.
Malbon had two more great efforts to score. However, Pickering was alive to them to keep the Newcastle lead intact.
However, the forward made no mistake on 86 minutes when a Kyle Diskin corner was played to him and, his shot hit the back of the net with aid of a deflection.
In the first minute of injury time, Grove should have had a penalty when Jennings was bundled to the ground. However, the referee wasn't interested in giving it.
The result means Kidsgrove will make the trip to Newcastle Town in 10-days time for a replay. While the home game against Chasetown on 2nd September will be postponed.
Kidsgrove Athletic: Harrison, Murphy, Morris, Hall, Duffy, Butler, Diskin, Blake (Wiggins-Thomas, 74), Adu-Gyamfi (Jennings, 62), Malbon and Williamson.
Subs not used: Bergin, Thompson and Rhodes.
Newcastle Town: Pickering, Melhado, Williams, Glover, Askey, Dennis, Needham (Ahmadi, 64), Bradbury, Cole, Ward and Conlon.
Subs not used: T. Van der Lann, Cartwright and Gill.
Attendance: 152