A penalty after 20 minutes which resulted in defender Greg Hay being sent off was the difference between the teams in the first Premier Division match of the new East of Scotland season.
Jamie Lauder scored from the spot after Hay was shown a red card for bringing down a Leith attacker who was in a goalscoring position.
It was a double blow for Neil Oliver’s men, but in truth they were lucky to go in at half time only 1-0 down at Meadowbank 3G after wave after wave of Leith attacks.
Only poor finishing and some outstanding goalkeeping from Coldstream’s Mark Walters kept the scoreline respectable.
The ten men managed to stem the tide somewhat in the second half and could have snatched an unlikely draw in the end.
Jack Hay missed a glorious chance to equalise just five minutes after the interval, his left-footed shot dragged wide of the post.
John Crawford missed from close range after being set up by Jonny Simpson, and Jake Rutherford squandered a late chance by finding the side netting when a cut-back was on.
Leith also had their chances in the second half, hitting the post with the best of them after Michael Allan had cleared off the line.
Coldstream: Walters, G Hay, Allan, Baxendale, Ainslie, Devaney, Douglas, J Hay, J Simpson, Lauder (Wales 20), Crawford. Subs: Powling, Rutherford, Graham.