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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.
The striker's second midway through the second half was shrouded in controversy as there appeared to be a handball in the build-up. But despite West Ham's protests the goal stood.
West Ham's only goal was in fact a Sydney own-goal as captain Nikola Petkovic deflected the ball into his own net.
It summed up West Ham's difficulties in the final third which were evident in their 2-1 defeat to the Wellington Phoenix on Wednesday night too.
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 Hammers midfielder Mark Noble to break clear. He threaded a great 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 to 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-Isei, who passed to an unmarked Brosque on the left side of the box. He took one touch they fired the ball into the bottom right hand corner.
Ten minutes before the break West Ham defender Aaron Cresswell, who had come on for Guy Demel in the 13th minute, saw his shot hit the side netting. It summed up a disappointing 45 minutes for the Hammers.
Mauro Zarate was brought on for Carlton Cole at half-time but it was an element of luck that got the Hammers on the score sheet when Petkovic deflected the ball into his own net off Jarvis' cross.
Abbas impressed for Sydney in his 63 minutes on the pitch. Aside from setting up Gameiro's opener, he had a long-range shot go just over the bar and also showed excellent touch to lay up for Antonis who then blasted the ball over.
Sydney substitute Peter Trantis saw another effort just kiss the crossbar in the 63rd minute before Gameiro grabbed his controversial second a minute later.
While the young striker showed coolness to round the keeper to score, replays suggested Antonis had handled the ball in the build-up.
It sparked protests from the English side but to no avail.
It was the last real action of the game as both sides turned to their benches and the match meandered to a low-key finish.
Full Time: Sydney 3 (Gameiro 4, 64, Brosque 26), West Ham 1 (Petkovic og 51). HT: 2-0 Sydney.
Hammered: West Ham stunned by Sydney FC
