Two goals shortly before half-time eased the pressure on under-fire Magpies boss Graeme Souness and turned a game that had begun to look difficult for the Premiership side.
Newcastle started positively enough but quickly became bogged down by the hard-running, chase-everything attitude of the home side.
In Kayode Odejayi, the Robins had the one player who looked capable of unlocking the Newcastle defence and he almost did so on two occasions when presented with his team's best chances.
In the first half, he produced a dart of pace to get beyond the two Newcastle central defenders and try a shot that skidded just wide of the target and then, late in the second half, he ran onto a pass from Craig Armstrong and rounded goalkeeper Shay Given only to blast his shot into the stand behind the goal.
By then Newcastle had taken control of the game having scored twice during the five minutes leading up to the break, although the goals had an element of fortune about them.
The first arrived on 41 minutes when Celestine Babayaro broke into the penalty area. Cheltenham goalkeeper Shane Higgs rushed out to dive at his feet and the ball spun up into the air. There seemed to be a moment's hesitation before Michael Chopra jumped ahead of a Cheltenham defender to head into the net.
Two minutes later Newcastle got their second goal when Peter Ramage delivered a cross from the right, Cheltenham right-back Jerry Gill attempted to volley clear but the ball struck Scott Parker and bounced over the line. Parker would have known little about it but must have been pleased to get onto the scoresheet following an injury lay-off.
Cheltenham battled manfully from that point onwards and enjoyed spells of prolonged pressure around the Newcastle penalty area but the Premiership stars had a little too much for the Coca-Cola League Two outfit.
Alan Shearer had a quiet game by his standards and still requires one more goal to break Jackie Milburn's all-time club record. His first-half bicycle kick flew high over the crossbar and he was inches away from making contact with a second half cross from Shola Ameobi that would have brought him the record in front of the Geordie fans in the stand behind the goal.