Backstrom scored with seven seconds left after Panik tied it 2-2 on the power play with 1:09 remaining.
Zach Sanford scored a power-play goal 2:05 into the third to give the Blues a 2-1 lead, and Austin Poganski scored in the first period for St. Louis. Jordan Binnington made 22 saves playing the first two periods. Evan Fitzpatrick made eight saves in the third.
Radko Gudas scored a second-period goal, and Alex Ovechkin had two assists for Washington. Vitek Vanecek made 13 saves playing the first half of the game; Ilya Samsonov made 11 finishing it.
The teams, winners of the Stanley Cup the past two seasons, open the regular season against each other at St. Louis on Oct. 2.
Video: Capitals rally past Blues with two late goals
Panarin injured in Rangers loss to Devils
Artemi Panarin sustained a mild groin strain after scoring in his preseason debut with the New York Rangers, a 4-3 loss to the New Jersey Devils at Madison Square Garden.
With the Rangers trailing 2-0, Panarin scored on the power play with a one-timer from the left face-off circle at 7:33 of the second period. Defenseman Jacob Trouba, acquired in a trade with the Winnipeg Jets on June 17, and forward Kaapo Kakko, the No. 2 pick of the 2019 NHL Draft, had the assists.
Panarin did not play the final 6:16 of the second period and sat out the third.
Nico Hischier, Mikhail Maltsev, Nikita Gusev and Brett Seney scored for New Jersey. Cory Schneider made 27 saves on 29 shots in the first two periods. Evan Cormier played the third and made 12 saves. Will Butcher and Sami Vatanen each had two assists.
Micheal Haley and Lias Andersson scored for New York, which was playing its first preseason game. Alexandar Georgiev allowed three goals on 11 shots in 30:10; Igor Shesterkin made 14 saves.
Video: Hischier, Gusev score as Devils defeat Rangers, 4-3
Canadiens score shorthanded to defeat Panthers at Hockeyville
Alex Belzile scored a tiebreaking shorthanded goal at 13:57 of the third period to give the Montreal Canadiens a 4-3 win against the Florida Panthers in the Kraft Hockeyville Canada 2019 preseason game at K.C. Irving Regional Centre in Bathurst, New Brunswick.
Jeff Petry and Matthew Peca each had a goal and assist for Montreal, which has won its first two preseason games. Riley Barber scored, and Charlie Lindgren made 17 saves.
Evgenii Dadonov and Jonathan Huberdeau each had a goal and an assist, Mike Hoffman scored, and Aaron Ekblad had two assists for Florida, which lost two split-squad games to the Nashville Predators on Monday. Chris Driedger made 15 saves.
The Canadiens and Panthers play at Montreal on Thursday.
Video: Canadiens rally in 3rd for 4-3 win in Renous
Hurricanes complete back-to-back shutouts against Lightning
The Carolina Hurricanes shut out the Tampa Bay Lightning in a second straight preseason game, 2-0 at PNC Arena.
Petr Mrazek made six saves in 30:22 and Alex Nedeljkovic made 15 in relief after James Reimer and Anton Forsberg combined for 15 saves in a 3-0 win at Amalie Arena on Tuesday.
Steven Lorentz scored at 4:53 of the first period, and Clark Bishop scored a power-play goal at 5:06 of the third.
Spencer Martin allowed one goal on 13 shots in 30:22, and Zach Fucale allowed one goal on 11 shots for Tampa Bay.
Hurricanes forward Erik Haula left for precautionary reasons with 9:08 remaining in the second period.
Matthews scores first in Maple Leafs loss to Senators
Brady Tkachuk had a goal and an assist to help the Ottawa Senators defeat the Toronto Maple Leafs 4-3 at Canadian Tire Centre.
Max Veronneau, Connor Brown and Tyler Ennis scored, and Mark Borowiecki had two assists for Ottawa. Craig Anderson saved 20 of 21 shots over the first two periods; Filip Gustavsson made 16 saves in the third.
Auston Matthews scored two goals and William Nylander had two assists for Toronto. Michael Hutchinson allowed three goals on 20 shots in two periods. Brandon Halverson made six saves in the third.
Matthews' first goal of the preseason made it 2-1 at 4:45 of the second period, but Ennis scored at 6:09 to make it 3-1.
Matthews scored to make it 3-2 at 7:27 of the third period. Tkachuk scored an empty-net goal at 17:43.
Video: Balanced effort lifts Senators by Maple Leafs, 4-3
Keith, Crawford help Blackhawks defeat Red Wings
Duncan Keith scored to break a tie midway through the second period, and the Chicago Blackhawks defeated the Detroit Red Wings 2-1 in a preseason game at United Center.
Brandon Hagel scored for Chicago, and Corey Crawford made 23 saves.
Taro Hirose scored a power-play goal for Detroit. Jonathan Bernier saved 10 of 11 shots in 30:05; Filip Larsson made 16 saves.
Keith scored off a pass from Patrick Kane at 10:55 of the second.
Video: Hagel, Keith score as Blackhawks down Red Wings, 2-1
Wheeler, Copp help Jets defeat Wild
Blake Wheeler and Andrew Copp each had a goal and an assist for the Winnipeg Jets in a 4-1 preseason win against the Minnesota Wild at Bell MTS Place.
Josh Morrissey scored a power-play goal, CJ Suess scored into an empty net, and Sami Niku had two assists for the Jets. Laurent Brossoit made 20 saves.
Nico Sturm scored for the Wild. Kaapo Kahkonen played the first two periods and allowed two goals on 20 shots. Mat Robson made 10 saves in relief.
Video: Wheeler, Copp lift Jets past Wild, 4-1
Gaudreau, Quine, Dube help Flames top Sharks
Johnny Gaudreau, Alan Quine and Dillon Dube each had a goal and an assist for the Calgary Flames in a 6-4 preseason win against the San Jose Sharks at Scotiabank Saddledome.
Dube's goal at 13:35 of the second period gave the Flames a 5-3 lead. Sean Monahan, Adam Ruzicka and Derek Ryan scored for Calgary, and Jon Gillies made 16 saves.
Manuel Wiederer scored twice, Ivan Chekhovich had a goal and an assist, and Lean Bergmann scored for the Sharks. Jayden Halbgewachs and Tony Sund each had two assists, and Antoine Bibeau made 17 saves.