Canada surrendered a lead late on to draw with tournament hosts Japan, while the USA suffered a shock 3-0 defeat to Sweden.
Beckie and Dahlkemper both competed 90 minutes, collecting their 76th and 72nd caps respectively, as 11 of our 12 City stars were in action ((including Team GB's win over Chile) on an entertaining day.
Looking to better their bronze medal finish at the 2012 and 2016 Games, Canada enjoyed a dream start to a thrilling clash at the Sapporo Dome, as Christine Sinclair struck her 187th goal on her 300th cap to open the scoring.
Barely five minutes had passed when the striker found the net, slotting home at the second attempt after her first effort from Nichelle Prince's cut-back had come back off the post.
Drama unfolded after the break when Japan were awarded a penalty following a VAR review, which ruled Stephanie Labbe had fouled Mina Tanaka.
The Canada goalkeeper stayed down with injury for a lengthy period of time but recovered to save Tanaka's resulting spot-kick, before being replaced by Kailen Sheridan.
Canada rallied and Beckie, employed on the right-wing, thought she had doubled the advantage from close range - only to be denied by the offside flag.
As the game entered its closing stages, Japan battled back as Mana Iwabuchi hit a late leveller, latching onto a long ball and clipping around Sheridan with six minutes of normal time remaining.
Despite eight minutes of stoppage time, neither side could find a winner and the points were shared in Group E.
Canada face Chile on Saturday 24 July in Matchday Two at 8:30 UK time.
Meanwhile, Dahlkemper's United States suffered a heavy defeat in Group G.
A brace from Stina Blackstenius and a Lina Hurtig header handed 2016 silver medallists Sweden victory, ending the World Cup winners' 44-game unbeaten run.
Dahlkemper, who has started 65 of her 72 caps, was named in the starting XI, alongside former City stars Sam Mewis and Rose Lavelle, while Carli Lloyd was also introduced from the bench.
Former City forward Kosovare Asllani lined-up for the Swedes.
The clash provided the USA with the chance for revenge for their penalty shoot-out defeat in the quarter-finals of the 2016 Games but they found themselves behind after 25 minutes.
Fridolina Rolfo had already forced Alyssa Naeher into a low stop, providing an early warning, before Blackstenius nipped in to head home Sofia Jakobsson's delivery.
Naeher was called into action again to deny Jonna Andersson, while Lavelle almost found a leveller on the stroke of half-time, striking the woodwork.
Sweden doubled the lead inside ten minutes of the restart as Blackstenius converted from close range, after Amanda Ilestedt's initial effort rebounded off the post.
As the USA pressed for a route back into the game, the ball found the woodwork once more, as Megan Rapinoe's cross hit Christen Press and bounced back, after Lloyd had watched an effort deflect wide.
Not two minutes later, it was 3-0 to Sweden as Hurtig powered home Hanna Glas' cross to seal the contest.
Press almost grabbed a late consolation but Hedvig Lindahl clawed the effort away to preserve a clean sheet.
The USA face New Zealand in Matchday Two on Saturday 24 July at 12:30 UK time.