The result was harsh on the home side, who displayed determination and plenty of quality in possession but were caught out by two incisive breakaway goals.
Scunthorpe defended with admirable resilience and displayed a ruthless streak in attack, scoring from the only two shots on target they mustered in the whole game.
Cheltenham certainly dominated the first half with Scunthorpe goalkeeper Joe Murphy having to save from Drissa Diallo and Ashley Vincent in the first 10 minutes.
On-loan striker Stuart Fleetwood just missed a cross from Vincent at the far post as Cheltenham threatened an opener, but with 34 minutes played it was the visitors who scored with their first chance of note.
Former Cheltenham midfielder Grant McCann won the ball in the centre of the pitch and supplied striker Gary Hooper and he raced away from the Cheltenham defence before planting a low shot past goalkeeper Scott Brown.
Cheltenham midfielder James Wesolowski sent a header into the side-netting right on the stroke of half-time, but the Robins kept plugging away and finally drew level 20 minutes from the end when substitute Paul Connor got up to head a corner from Alan Wright into the net from close range.
Sensing the possibility of victory, Cheltenham manager Martin Allen committed further resources to attack in the final 20 minutes.
However, they were vulnerable to the breakaway and almost conceded a goal 10 minutes from time when central defenders Diallo and Darren Kenton got into a muddle leaving Sparrow clean through on goal.
Brown saved his team with fine goalkeeping to deny both Sparrow and substitute Ben May.
But that proved merely a stay of execution because, with two minutes of injury time played, a long clearance from Murphy was flicked on by May and Sparrow kept a cool head to beat Brown.