The City star, winning her 77th cap, was at the centre of the action at the Sapporo Dome, striking in both halves after earlier seeing a penalty strike the post.
Having drawn their opening Group E game 1-1 against hosts Japan on Wednesday, Canada – bronze medallists in both 2012 and 2016 – were seeking a positive response.
After a bright start they were awarded a 19th minute penalty with VAR confirming the spot-kick after Christine Sinclair was brought down in the box.
Beckie struck the penalty sweetly but her effort rebounded back off the post.
However, six minutes before the break Beckie more than made amends.
The City star reacted smartly after Nichelle Prince’s cross rebounded into the middle of the box, firing home a superb finish to break the deadlock.
Two minutes after the restart Beckie struck again to double Canada’s advantage.
Prince was again the architect, supplying an inviting ball over the top of the Chilean defence and Beckie timed her advancing run to perfection to pounce and beat the keeper.
However, Chile gained a foothold on 57 minutes when they were awarded a penalty of their own after a Zadorksy foul and Karen Araya converted to set up a tense last half hour.
Both sides came close in a pulsating finale with Chile hitting the bar and Sinclair’s goalbound effort deflected wide.
But Canada held firm to claim a crucial victory and set up an intriguing third and final group game against Team GB in Kashima next Tuesday, kick-off 12pm (BST)
Meanwhile, Abby Dahlkemper played the full 90 minutes as the USA bounced back in emphatic style from their opening day loss with a 6-1 rout of New Zealand in Group G.
Seeking a quick response after a shock 3-0 loss to Sweden last Wednesday, the world champions were in ruthless form in Saitama.
Former City midfielder Rose Lavelle opened the scoring with a ninth minute finish, latching onto Tobin Heath’s assist and from there on in the Americans never looked back.
Lindsey Horan added a second on the stroke of half-time with a header to mark her 100th cap in fitting fashion.
With another former City star Sam Mewis making a second half appearance from the bench, the United States further extended their advantage after the break thanks to an Abby Erceg own goal just past the hour mark.
And though Betsy Hasset reduced arrears on 72 minutes, Christen Press restored the three-goal advantage 80 minutes.
A dominant American display was then wrapped up with two more late goals from Alex Morgan and a second own goal to leave Team USA second in Group G with three points ahead of their final group match against Australia on Tuesday, kick-off 9am (BST).