The union will now ballot workers at two other M&E giants over plans to withdraw from the JIB pay and conditions agreement and replace it with the new BESNA deal.
The next firms facing a ballot are believed to be NG Bailey and Crown House.
Balfour is planning to seek an injunction against the ballot on the grounds the vote was flawed.
The Unite members at BBES voted by 81% for strike action with 360 voting ‘yes’ and 81 ‘no’.
A BBES statement said: “Balfour Beatty Engineering Services is disappointed that a small percentage of employees have voted in favour of strike action.
“Just over 21% of our employees affected by the BESNA (from a total of 1,650 workers) voted in favour of strike action.
“We have strong grounds to believe that Unite’s strike ballot procedures were flawed and BBES plan to request the court to take out an injunction in the next few days.”
Unite national officer, Bernard McAulay, said: “This is a resounding result and shows our members have not been conned and therefore Balfour Beatty Engineering Services need to recognise they do not have the support of their employees.
“Unite therefore calls on Balfour Beatty to immediately engage in discussion with the union to find a sensible solution to this dispute.”
Unite will be announcing dates for strike action in due course.
HVCA chief executive Blane Judd said: “Unite’s strike mandate was achieved through the use of misleading and unjustified scare tactics.
“We hope that Balfour Beatty’s workers will communicate with their employer to get the facts about the proposed Building Engineering Services National Agreement (BESNA) before deciding to strike.
“However, it’s important to remember that the other six companies supporting the BESNA are not affected by this action and are proceeding with their employee consultations.
“We remain confident that the new agreement is the best way to secure jobs, develop skills and compete effectively against foreign firms.”