They have now taken four points from two games, but Coldstream could not hide their disappointment after squandering a two-goal lead and missing a penalty.
Stevie Gibbard’s men fell two points behind their nearest rivals at the bottom of the table after Craigroyston’s unexpected victory.
But is was their failure to capitalise on such a good start to this game which was the biggest letdown.
Regan Graham, inset, and John Crawford put the Streamers two ahead inside the first 20 minutes, but the visitors pulled one back and dominated most of the second half.
James Guy’s equaliser was well deserved, but Crawford then had a chance to put Coldstream back in front from the penalty spot.
The spot kick was awarded when left-back Michael Allan was tripped in the box after a surging forward run. But Crawford’s effort from the spot was well saved by the Civil Service Strollers goalkeeper.
With both sides going for the win in the closing stages, there were chances at both ends. But the best of them fell to the visitors, who were unable to get past Coldstream goalkeeper Mark Walters.
In the end, Gibbard’s men were perhaps relieved to pick up a point. Under pressure for much of the second half, they could easily have lost this.
It was a different story in the opening 20 minutes when Coldstream were direct, quick to the loose ball and purposeful in attack.
The opener was superbly taken by Graham, who timed his run off the left flank to perfection. The ball had been played up to Luke Strangeways in attack. After bringing it down on his chest the forward from Wooler hooked into the path of Graham running between the Strollers centre-backs. The youngster showed composure to pass the ball into the corner of the net.
Crawford doubled the lead with a typically powerful header from a superb cross delivered from the right flank by Craig Heugh.
But new Strollers signing Scott Gormley fired a 20-yard shot into the top corner to pull one back in 35 minutes. Guy, a former Coldstream player,lashed home the equaliser in 65 minutes.
Coldstream’s Josh Hebdon was sent off in the closing minutes for a second bookable offence.
Coldstream: Walters, McLeod (Johnson 78), Allan, Ainslie, Dixon (O’Neil 78), Neil, Heugh, Hebdon, Crawford, Strangeways, Graham (J Simpson 55). Subs not used: Rutherford, Clowes.