Two goals in five minutes midway through the second half saw The U's get the better of their highly-fancied opponents at The Pilot Field.
Tony Dolby's side had much of the better of this Ryman Premier contest but had to wait until the hour mark to make the breakthrough when captain Sean Ray headed home a Russell Eldridge free kick.
Soon after debutant Kenny Pogue scored just seven minutes after coming off the substitutes' bench by firing in off the crossbar following Michael Phillips' flick on.
Hastings had their moments in the first half with Ade Olorunda causing all sorts of problems in the final third.
The striker was denied by a fine parry from Jonathan North before so nearly combining for the opening goal with Sam Adams who also had an effort saved.
Olorunda also fired wide from the edge of the box with only North to beat after being set up by the impressive Eldridge.
Wealdstone's best spell came in the opening 20 minutes but once Ray and John Beales had got to grips with the visiting attack, they rarely threatened Clark Masters in the Hastings goal.
Hastings: Masters, Jirbandey, Elford, Beales, Ray, Storey (T. Olorunda 92), Cade (Pogue 58), Phillips, A. Olorunda (Logan 80), Adams, Eldridge. Subs not used: Russell, Chalmers-Stevens. Attendance: 563.
TODAY'S FOOTBALL RESULTS
Ryman League, Premier Division: HASTINGS UNITED 2 Wealdstone 0.
Sussex County League, Division 1: Redhill 0 RYE UNITED 1; Three Bridges 4 SIDLEY UNITED 3.
Division 2: Loxwood 1 BEXHILL UNITED 0; Storrington 0 LITTLE COMMON 1; WESTFIELD 2 Littlehampton Town 0.