Canada were awarded the penalty by Ukrainian referee Natalia Rachynska after Adriana Leon was fouled by Rong Zhao.
The sell-out crowd of 53,058 at the Commonwealth Stadium in Edmonton, the largest for a national team sporting event in Canada, roared when Sinclair’s shot sailed past goalkeeper Wang Fei.
Sinclair’s goal eased the host’s frustration after they had toiled to score despite having the bulk of chances in the Group A encounter.
Following the gala opening ceremony, China came closest to scoring with a first-half free-kick that bounced off both posts.
It was the first match of the month-long tournament that will be played across six Canadian cities. The United States open their campaign early tomorrow morning against Australia and the final is set for 5 July in Vancouver.
The pressure is on Canada, ranked eighth in the world and making their sixth World Cup appearance. Their best finish was fourth in 2003.
Canada have been on the rise in recent years under head coach John Herdman and have also seen increased support by the government in advance of the World Cup.
The team claimed a surprising bronze-medal finish at the 2012 London Olympics.
Sixteenth-ranked China are returning to the expanded 24-nation World Cup after missing out in 2011, when 16 teams contested the tournament in Germany.
Known as the Steel Roses, China’s best World Cup finish was second in 1999, when the team fell to the United States in the final at the Rose Bowl in Pasadena, California.
Sinclair had a chance in the eighth minute but her strike sailed just wide and past the outstretched arms of China’s goalkeeper Wang.
Gu Yasha then threatened for China but Canada goalkeeper Erin McLeod came far off her line to stop the attack in the 18th minute.
China’s Wang Lisi’s incredible free-kick just minutes later bounced between both posts but didn’t cross the goal-line.
Sinclair got a couple of chances late in the match, including a shot off a pass from Sophie Schmidt that was scooped up by Wang.
Top-ranked Germany are among the tournament favourites, along with the second-ranked Americans and France. Japan are the defending world champions after beating the United States on penalty kicks in the 2011 final.
In the other Group A match on Saturday night, Lieke Martens’ long strike from outside the box in the first half gave the Netherlands their first Women’s World Cup goal and a 1-0 victory over New Zealand.
Martens curled the ball up and over the outstretched arms of New Zealand goalkeeper Erin Nayler in the 33rd minute. The Netherlands are one of eight teams making their debut in the World Cup.
In last night’s opening Group B game Norway beat Thailand 4-0. Norway’s goals came from Trine Ronning, Isabell Herlovsen (2) and Ada Hegerberg.