Marcello Lippi's side were emphatic victors at the Tianhe Stadium on Sunday as they maintained their six-point advantage at the top with three matches remaining.
Elkeson's second-half double also leaves him on the verge of a personal record, the Brazilian needing just one more goal to break Li Jinyu's record of 26 in a campaign set in 2006.
Yu Hanchao put the league leaders ahead with a neat finish on 11 minutes and Evergrande remained one goal to the good at the break.
Elkeson's first came four minutes before the hour mark as he pounced on a loose ball inside the penalty area to fire low into the bottom corner from 12 yards.
Alessandro Diamanti rounded things off in stoppage time and Evergrande retain a healthy lead over Beijing Guoan at the summit.
Guangzhou R and F got back to winning ways against Guizhou Renhe, a 1-0 victory keeping Sven-Goran Eriksson's men on course for a top-three finish.
Abderrazak Hamdallah struck the only goal of the game on 31 minutes as R and F put their derby defeat to Evergrande behind them.
Harbin Yiteng suffered another blow in their fight for survival as they lost 2-1 to Shanghai Shenhua and had Dori sent off for two bookable offences.
Harbin remain at the foot of the table, six points from safety, but Henan Jianye climbed out of the bottom two with a win over fellow strugglers Liaoning Whowin.
Rafael Marques' strike gave Harbin a 1-0 win and saw them climb two places in the table, dropping Shanghai Shenxin into the relegation places.
Elsewhere, Changchun Yatai and Tianjin Teda could not be separated in a game that finished 1-1 and Dalian Aerbin rescued a 2-2 draw against Jiangsu Sainty thanks to Bruno Meneghel's stoppage-time penalty.
