The result was the Premier League outfit's second in succession to A-League opposition, after their 2-1 reverse to Wellington Phoenix on Wednesday.
Gameiro got his opener in just the fourth minute and Alex Brosque slotted home to give the Sky Blues a 2-0 lead at the break.
West Ham hit back early in the second half, when Sydney captain Nikola Petkovic deflected the ball into his own net.
Gameiro's second sealed the win for Sydney midway through the second half, although the goal was shrouded in controversy as there appeared to be a handball in the build-up.
The result summed up West Ham's difficulties in the final third which were evident in their loss to the Phoenix.
The two losses, coupled with key striker Andy Carroll being ruled out for four months following ankle surgery, are sure to ramp up pressure on manager Sam Allardyce with the opening game of the Premier League season against Tottenham just three weeks away.
Sydney, who lost 4-0 to Newcastle United in the opening match of the Football United Tour on Tuesday night, got off to the dream start.
Having successfully defended a free-kick from right on the edge of their own box, Ali Abbas pounced on a loose pass from West Ham midfielder Mark Noble to break clear and threaded a pass to Gameiro who coolly slotted it past Adrian.
Allardyce bemoaned his side's lack of finishing against the Phoenix and he would have been left equally frustrated with his side's wastefulness at Westpac Stadium.
Noble fired a free-kick from just outside the box straight at Sydney keeper Vedran Janjetovic in the 19th minute after a heavy challenge on Matt Jarvis by Terry Antonis.
Hammers midfielder Mohamed Diame then wasted a gilt-edged chance four minutes later when having dispossessed Milos Dimitrijevic he scuffed his shot straight at the Sky Blues keeper.
Sydney made the Premier League outfit pay in the 26th minute as they doubled their lead.
This time it was a counter-attack from Bernie Ibini, who passed to an unmarked Brosque, who took a touch and fired the ball into the bottom right hand corner.
West Ham were back in the game in the 50th minute, when Petkovic deflected a Jarvis cross into his own net, but Gameiro's controversial second goal 15 minutes later sealed the win for the A-League outfit.
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