Goals from Sophie Schmidt and Martina Franko on 55 and 77 minutes added to Sinclair's clinicically-taken double and left the Black Queens on the brink of elimination - a fate subsequently confirmed by Australia's draw with Norway later in the evening. For the African contenders, it is their third successive first-round exit and means Wednesday's match against Norway will be their last here in China.
As for Even Pellerud's side - a point behind Australia and Norway going into Wednesday's showdown with the Matildas - they will live to fight another day after dominating a match they led from just after the quarter-hour mark, when Gladys Enti just could not get enough of a touch to prevent Sinclair's looping header crossing the line.
Ghana missed an incredible chance to go into the break level when Anita Amankwa rattled the crossbar from all of two yards but the writing was on the wall from the moment Schmidt reacted first to head home a Kristina Kiss corner nine minutes after the restart.
Sinclair then completed her brace, profiting from some superb approach play by Kara Lang to side-foot emphatically home, before another Kiss corner evaded Enti and left Franko with the simplest of tasks to nod over the line.
Player of the Match: Christine Sinclair (CAN)