Tancredi's goals in the 43rd and 83rd minutes enabled Canada to overcome a two-goal deficit after 16 minutes and earned it a knockout round match on Friday against host Britain.
It advanced to the final eight along with CONCACAF rival and the two-time defending champion United States, which completed its first round with a 1-0 victory over North Korea later Tuesday and will face New Zealand in the quarterfinals.
Canada, which was eliminated in the quarterfinals in extra time four years ago in Beijing by the United States, finished in third place in Group F with four points, one behind Sweden and Japan.
In Newcastle, England, Christine Sinclair had a hand in both of Tancredi's goals, getting a touch on the first that sent the ball wide to Rhian Wilkinson. Wilkinson crossed it to the middle of the box, where ball took a bounce and Tacredi volleyed it into the side netting from just outside the six.
Then, with Canada dominating possession in the second half, Sinclair created space for herself outside the area and crossed a high ball to the back post where Tancredi headed inside the right upright.
Canada had the better of play early, exploiting the flanks and including Sweden's clearance off the line of a Jonelle Filigno shot. But the North Americans fell behind on a goal and an assist by Marie Hammarstrom in the 14th and 16th minutes.
Hammarstrom was able get beat Wilkinson to Lina Nilsson's low cross and get the outside of her left foot to the ball at the six, beating Canadian keeper Eric McLeod.
Less than two minutes later, Hammarstrom sent a ball across the face of goal that McLeod came off her line to punch, but missed, the ball bounced through the legs of defender Lauren Sesselmann and continued on the back post where Sofia Jacobsson touched it in.
In Manchester, Abby Wambach scored in her third straight game and goalkeeper Hope Solo extended her shutout streak to 256 minutes to lead the Americans past North Korea and finish atop Group G.
In a rainy Old Trafford stadium, the Americans outshot the Koreans 17-3 and hit the post twice to win their third consecutive match.
It was the United States' fourth victory five matches against North Korea - with one draw. All previous meetings were in the Women's World Cup.
The Americans dominated from the start, forcing Korean keeper O Chang Ran to tip Alex Morgan's drive around the left post in the fifth minute.
Morgan would hit the post before she set up Wambach for the lone goal in the 25th minute.
Lauren Cheney looped a ball into the penalty area where Morgan settled, drew two defenders to herself and then slipped a short ball between them to Wambach, who was left alone in front five meters from goal.
North Korea finished the match with only 10 players after Choe Mi Gyong was ejected in the 81st with a second yellow card, the last for a foul tackle on Cheney.
The United States earned eight corners while North Korea didn't generate any.
Solo saw few challenges and hasn't allowed a goal since the 14th minute of the United States' 4-2 opening victory over France.