The Swedes also go through as Group F winners after Japan could only draw 0-0 with South Africa, though the Scandinavians will know that better is required in the knockout stages after this unconvincing showing.
Canada dominated the game’s early stages, and might have taken the lead after just six minutes when the sliding Tancredi just missed out on making contact with Christine Sinclair’s inviting right-footed cross.
The 31-year-old had been on target in each of her team’s opening two matches and she threatened again five minutes later when only a goal-saving clearance from Lina Nilsson prevented the Canuck striker making it three in three.
Yet it was after these chances, and 14 minutes of near-total Canadian domination, that Sweden took the lead. This time Nilsson was involved at the other end, crossing from the right for Marie Hammarstrom to prod home left-footed from seven yards.
It was a stunning blow for John Herdman's side, and their gloom was to deepen inside two minutes when the Swedes doubled their lead.
This time Hammarstrom was in the role of creator, tempting Erin McLeod out of her goal with a tantalising left-footed cross that, having been missed by the Canada goalkeeper, ricocheted off the shins of Sofia Jakobsson and into the net.
That second goal seemed to knock the stuffing out of Herdman’s team, but just as they appeared to be running out of ideas, Tancredi handed them a lifeline.
A fine move down the right culminated in long-awaited success, with Rhian Wilkinson’s deep cross diverted into the back of the net by the predatory No14.
The Canadians now knew that one more goal would see them through to the quarter-finals and, after Johanna Almgren had sliced wide a glorious opportunity to seal the points for Sweden, Tancredi struck again with seven minutes remaining, diving in to head a goal that sparked delirium on the North Americans' bench.