Ghana were unlucky not to go in to halftime level at 1-1 when a rare attack ended with the ball crashing off Canada's cross bar just before the break after a good cross from Ghana captain Adjoa Bayor.
Canada, who lost 2-1 to Norway after leading 1-0, were determined not to make the same mistake against Ghana, the lowest ranked team in the tournament.
Sophie Schmidt, Canada midfielder, doubled her side's lead on 55 minutes when she headed past keeper Memunata Sulemana from a failed corner clearance, before Sinclair blasted home her second in the 62nd minute after Kara Lang rounded the defence, leaving her skipper with an easy volley to goal.
Poor goalkeeping by Sulemana gifted Canada their fourth when she failed to collect a corner allowing Martina Franko to head in the loose ball from close range.
New Zealand also out
Meanwhile in Wuhan, the highly fancied Denmark had to work hard to overcome a gritty New Zealand side 2-0, thus knocking the Oceania nation out of the competition with two losses from two matches.
After a scoreless first half, Katrine Pedersen, Denmark captain, scored with a well-struck free kick in the 61st minute after New Zealand's Maia Jackman was booked for a questionable foul on striker Maiken Pape near the penalty box.
Denmark then put the result beyond doubt five minutes later as a tiring New Zealand were again penalised, once more paying dearly for their errors when Cathrine Paaske Sorensen clipped her header home.
Denmark move to three points after losing their opening match to hosts China 3-2.
Brazil run riot, Aussies snatch draw
Australia's 'Matildas' celebrate a late equaliser
against Norway in Hangzhou [AFP]
In the later matches on Saturday, Brazil thrashed China 4-0 to dent the home team's hopes of qualifying for the quarter-finals as Australia snatched a late 1-1 draw against former champions Norway.
China began the tournament with a win over Denmark, but it all went horribly wrong against Brazil with the South Americans scoring three goals in six minutes to leave the hosts reeling.
The masterful Marta began the onslaught in the 42nd minute when she chased down a loose ball to ankle-tap it past charging goalkeeper Han Wenxia, before Cristiane scored the second and third in the 47th and 48th minutes respectively.
Marta made it four with 20 minutes to go, silencing a near-capacity crowd at the 52,000-seat Wuhan Sports Centre Stadium.
Meanwhile in Hangzhou, Norway, who won the World Cup in 1995, looked to have the match wrapped up after a fifth minute goal by Ragnhild Gulbrandsen, but Lisa De Vanna scored an equaliser with just seven minutes remaining.
A resurgent Australia, who won their first World Cup match after 12 years of trying in their opener against Ghana, lead Group C with four points, ahead of Norway on goal difference.