Frenchman Arnaud Gauthier scored on his debut as Coldstream cruised through to the second round of the King Cup to extend their unbeaten run to three matches.
Stevie Gibbard’s men were only one up at half time and took 53 minutes to double their lead after missing a glut of chances.
The visitors went ahead after 11 minutes when striker John Crawford headed home Jamie Dixon’s deep cross from the right.
The Streamers doubled their lead eight minutes into the second half when Crawford’s shot was well saved by debutant Hawick goalkeeper Scott Connington. Luke Strangeways stabbed home the rebound despite protests that he was offisde.
Crawford grabbed his second goal of the game after being set up by former Hawick forward Kris O’Neil.
The pick of the goals, however, came from Jonny Simpson. He cut in from the left wing and skipped past a Hawick defender before finding the far corner of the net.
Hawick’s Andy Noble rattled the post at the other end before Coldstream went nap.
Gauthier, one of four new French players Coldstream hope to sign, came off the bench to score with a header on his debut, just 24 hours after signing.
Hawick’s consolation came in the last minute. Gary Shillinglaw swung over a cross and Nicky Cairns did the rest by driving a shot into the net.
Albert defender Calvin Muttit said: “We played some good football and had chances. Coldstream’s second goal was a big turning point as it seemed to be offside.
“Our lack of fitness let us down, though, as we tired badly towards the finish.”
Hawick Royal Albert: S Connington, C Muttit, G Shillinglaw, R Fleming, S McKenzie, G Summers, P Brown, N Cairns, N Ramsay, M Smith, A Noble. Subs: S Russell, G Chadwick, M Stewart.
Coldstream: M Walters, J Dixon, K Ainslie, M Allan, P Tweddle, R Graham (J Oliver 76), J Rutherford (K O’Neil 55), K Neill, J Crawford, L Strangeways (A Gauthier 55). Subs not used: R McLeod, S Gibbard.