Wei Shihao and Zhang Yuning scored either side of the break at Sydney's Stadium Australia in a wake-up call for the tiny country ahead of its debut appearance at the global showpiece in North America in June-July.
Curacao, with a population of just 156,000, is the smallest nation ever to make a World Cup.
Despite this they came through CONCACAF qualifying unbeaten under Dutchman Advocaat with three wins and three draws and the experienced 78-year-old was expected to be at the helm when they create football history.
But he unexpectedly left last month to care for his ill daughter and was replaced by Rutten.
It proved to be a losing start for the former FC Twente, PSV Eindhoven, Feyenoord and Schalke coach, whose side are in a challenging Group E at the World Cup alongside Germany, Ivory Coast and Ecuador.
China, who failed to qualify for the World Cup, dominated the early exchanges in the friendly match that is part of the FIFA Series 2026.
But it was Curacao who had the first sniff of goal with former Birmingham City midfielder Juninho Bacuna's long-range strike narrowly missing the upright.
China, ranked 93 to Curacao's 81, had to wait until the 40th minute for their first clear chance when Wang Shangyuan blazed over the bar.
But when another came in first-half stoppage time they made it count.
Goalkeeper Yan Junling sent a long ball forward and it was headed into the path of Wei to finish beautifully.
China doubled their lead in the 59th minute when skipper Zhang latched onto a poor clearance in the box and fired into the right-hand corner, with an increasingly frustrated Curacao having no response.