Already relegated Cheltenham offered some resistance in the early stages with Michael Townsend and Andy Gallinagh both testing goalkeeper Josh Lillis, who was deputising for the injured Joe Murphy.
But Scunthorpe took control with two goals in four minutes just before the break. Striker Paul Hayes netted his 20th goal of the season when he forced the ball home from close range after 36 minutes.
The Iron captain Cliff Byrne made it 2-0 in the 40th minute when he thundered an angled drive past goalkeeper Scott Brown for only his third goal for the club.
The second half was largely one-way traffic with Cheltenham struggling to keep the home side at bay.
Keeper Brown produced a couple of great saves to keep out efforts from first Garry Thompson and then Sam Togwell.
But he could do nothing in the 67th minute when Arsenal loanee Lansbury showed good footwork in the box before finding the net with a fierce right-foot shot.
But the game ended on a sour note for Lansbury when he was stretchered off in stoppage time and taken to hospital for an X-ray on a knee injury.
He was hurt in a challenge from Yuri Berchiche, on loan at Cheltenham from Arsenal's fierce London rivals Tottenham Hotspur, who was shown a yellow card by referee Andy Hall.
But, before play could restart, Berchiche was taken off by Robins boss Martin Allen leaving his side to play with ten men for the final few seconds.