Denmark 1 Scotland 0
Schalke striker Sand climbed off the bench and headed home the winner on the hour.
Scotland had chances of their own, with James McFadden showing his quality on more than one occasion, and Berti Vogts will be pleased with the display if not the result.
McFadden had a chance in the opening seconds, but he dallied and failed to hit the target.
Milan forward Jon Dahl Tomasson should have opened the scoring for Denmark on nine minutes, but he took an age to pick his spot when well clear and duly fired against the outside of the post.
McFadden and Darren Fletcher had further chances for Scotland, while Denmark thought they had won a penalty on the stroke of half time, as Martin Jorgensen appeared to be felled in the box by Steven Pressley, but their protests were ignored.
Denmark coach Morten Olsen threw on Sand for the second half and he proved his worth by showing too much strength for Pressley before heading home from Jesper Gronkjaer's cross.
Gronkjaer almost doubled the advantage, but his rasping drive was tipped onto the bar by Paul Gallagher.
Aston Villa keeper Thomas Sorensen had to be alert to twice deny the lively McFadden, but it was in truth a comfortable evening for the Danes who can now look towards Euro 2004 with confidence.