Sean and Jonny Simpson both scored twice as Coldstream fought back from two down to win at Home Park.
The result means Neil Oliver’s men need just a point in their final fixture to win group D of the East of Scotland Qualifying League and secure a home tie in the last eight.
Oliver would have been impressed by the fighting spirit and strength in depth of his squad against opponents flying high in the First Division.
In what was only his second game in charge, the new manager was forced to make six changes to his starting line-up due to the absence of eight players for various reasons.
When the visitors took the lead after just two minutes it looked like Coldstream were in for a long afternoon.
Helped by the strong wind, a long kick from goalkeeper John Falconer cleared the home defence to send Mark Brown clean through and he coolly slotted low into the net.
John Hunter side-footed into the bottom corner in the 33rd minute after the Streamers were caught in possession on the edge of their own box.
But good work from Sean Simpson inside the Easthouses penalty area set up striker partner and namesake Jonny Simpson to pull one back before half time.
A through-ball from Andrew Douglas released Jonny Simpson to round the keeper and slide home the equaliser just three minutes into the second half.
Although there were chances at both ends after that, it looked like being a draw.
But Jonny Simpson turned provider in the 87th minute to punish the Easthouses defence and goalkeeper for hesitation inside their box. A quick lay-off allowed Sean Simpson to fire home from 16 yards.
Sean Simpson then ran on to Josh Hebdon’s lofted pass in injury time to lob Falconer and complete a double of his own.
Coldstream: M Walters, G Wales, R Baxendale, M Allan, J Birkett, A Hunter (Trialist 59), J Hebdon, A Douglas, S Simpson, J Simpson, G McCrudden. Sub not used: P Johnson.