Ryan McLeod scored, and Mikko Koskinen made 24 saves for the Oilers (18-13-2), who are 0-2-2 in the first four games of a five-game road trip and 2-8-2 in 12 games since Dec. 3.
"I thought we did a lot of things well tonight," Edmonton coach Dave Tippett said. "Our goaltender wasn't very good, and we didn't find enough pucks at the net to get us back in the game."
New York has won its past two games without forward Artemi Panarin, who was placed in NHL COVID-19 protocol prior to the game Sunday.
Alexis Lafreniere had a goal and an assist playing in Panarin's spot on the second line with Strome and Barclay Goodrow, who also had a goal and an assist.
"Honestly, they're very easy to play with," Strome said. "Goodrow just does all the right things all over the ice. He's so responsible, such an underrated player. The way he sees the game and reads the play, he's got a great stick, he breaks up a lot of plays and he's got underrated skill. 'Laffy,' you see the playmaking tonight, the ability. He made so many great plays tonight that could have resulted in more points for himself.
"A little bit of confidence, a little bit of swagger for those guys."
Kreider scored a power-play goal at 3:32 of the third period with a net-front deflection of Fox's initial shot to give New York a 3-1 lead.
He's the fourth player with at least 20 goals this season and has scored 12 on the power play, second in the NHL behind Oilers forward Leon Draisaitl (13).
Georgiev preserved the two-goal lead with a point-blank glove save on Connor McDavid at 11:33.
Strome scored less than three minutes later when his cross-ice pass redirected in off Oilers defenseman Tyson Barrie to give New York a 4-1 lead at 14:11.
"It's been frustrating, and I think it's kind of affecting our play now," Oilers defenseman Cody Ceci said. "Tonight, we were right there, we start taking a few too many penalties, their power play was moving it around really well, and it ended up costing us the game."
McDavid and Draisaitl, the top two scorers in the NHL with 53 and 52 points, respectively, were held off the score sheet in the same game for the fourth time in the past 12; it happened once in Edmonton's first 21 games.
"They're great players, they get their scoring chances, but we did a great job tonight," Rangers coach Gerard Gallant said. "It wasn't about one line or one player, it was about a team group, and they did a great job."