Marcello Lippi's men struggled to get into their stride in the early stages and had to wait until eight minutes into the second half to break the deadlock through Rene Junior.
Feng Renliang doubled the advantage 10 minutes later before Dong Xuesheng rounded off the scoring against last year's China League One champions.
Evergrande have now gone 21 home games unbeaten in the league.
Harbin Yiteng, who came up alongside Henan last term, were in action against 2013 runners-up Shandong Luneng on Friday, and looked to be heading for a hard-fought away point.
However, Harbin had Li Xudong dismissed for a second yellow card with three minutes remaining and Junior Urso took advantage by breaking the deadlock to spare the hosts' blushes.
Two other teams got their season off to a winning start on an opening weekend that saw four fixtures end all-square.
Beijing Guoan - third last season - triumphed 1-0 over Changchun Yatai, with Pablo Batalla scoring the solitary goal in the 67th minute.
The other victory went to Shanghai Shenhua, for whom Gao Di netted either side of the break in a 2-0 win at Shanghai Shenxin.
Guizhou Renhe made a disappointing start as they were held to a goalless draw at Jiangsu Sainty, while Huangzhou versus Dalian Aerbin was one of three fixtures to end 1-1 - Bruno Meneghel equalising after Wang Song had put the hosts ahead.
Shanghai SIPG's trip to Liaoning Whowin also resulted in a goal apiece, together with Tianjin Teda's game at home to Guangzhou R&F.
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