Both goals came during a four-minute spell in the second half, with Argentinian playmaker Dario Conca opening the scoring for Marcello Lippi's side from the penalty spot in the 72nd minute before Brazilian Elkeson, making his debut in the competition, added a second soon after.
The victory leaves the runaway Chinese Super League leaders in a strong position heading into next month's return leg in Qatar, with a semi-final against Kashiwa Reysol or Al Shabab awaiting the winners.
That quarter-final tie is locked at 1-1 following today's first leg at the Hitachi Kashiwa Stadium in Japan.
Hosts Kashiwa took a 21st-minute lead through Japan striker Masato Kudo but Saudi Arabian visitors Al Shabab drew level with a potentially valuable away goal just before half-time when Fernando Menegazzo found the back of the net with a superb volley.
Khosro Heydari scored the only goal as two-time Champions League winners Esteghlal secured a narrow advantage in their quarter-final against Thai FA Cup holders Buriram United.
Heydari's fortuitous strike came after just 90 seconds at Tehran's Azadi Stadium, with the defender mishitting a cross which then struck the left post and turned into the net.
Last year's runners-up Al Ahli left it late to rescue a 1-1 draw at home to K-League champions FC Seoul.
The Saudi Arabians trailed after just 10 minutes to Dejan Damjanovic's goal, but hit back 10 minutes from time thanks to substitute Sultan Al Sawadi.
Wednesday's AFC Champions League Results
Al Ahli 1-1 FC Seoul
Kashiwa Reysol 1-1 Al Shabab
Guangzhou Evergrande 2-0 Lekhwiya
Image courtesy of WSG