Albion and Crawley landed plum home ties in the FA Cup third round draw.
But Hastings missed out on a glamour incentive to win their replay against Harrogate.
Albion entertain Newcastle at The Amex for the second season running after knocking them out 1-0 in the fourth round last year with a late Will Buckley goal.
Crawley's reward for seeing off Chelmsford in round two is a visit from Premier League strugglers Reading.
Hastings have another long trip to Albion's Championship rivals Middlesbrough if they get past Harrogate in their home replay following yesterday's 1-1 draw in Yorkshire.
The ties will be played on January 5 and 6.