Captain Victoria Svensson did the damage for Sweden in the 50th minute, hammering home from close range, only for minnows Nigeria to come roaring back in the dying stages of the match.
Sweden finished runner-up at the last World Cup to Germany and spearheaded by veteran Svensson are desperate to go one better in China.
But the world number three faces a tough battle on the road to the finals, grouped with two-time World Cup winners the United States and Asian dynamos North Korea who drew 2-2 in their first outing earlier Tuesday.
Sweden now take on the Americans on Friday while the five-time African champions face North Korea in a double header in Chengdu.
Svensson, playing in her 138th international, latched onto a pass from Frida Ostberg to score her 59th international goal and put her team ahead.
The goal bolstered the Swedes after both sides came close in the first 45 minutes.
Caroline Seger hoisted a header over the bar in the 57th minute, and Svensson had looked dangerous again in the 70th when she placed her header over the bar after a pintpoint cross from tireless midfielder Charlotta Schelin.
But Nigeria never gave up, and Cynthia Uwak, the African player of the year who plies her skills in Europe, made no mistake when Sweden failed to clear in the penalty area, firing into the net from close range.
Nigeria have competed at every World Cup but have only reached the last eight once.
The team were in rapture after getting a draw, celebrating with a dance on the ground, much to the delight of the 20,000-strong crowd who turned out to watch the match in drizzling rain.