"It was a good test," Khabibulin said. "We really wanted to see where we're at. So it feels good to beat one of the best teams in the league."
Taylor Hall also scored for the Oilers (5-2-2), who have won three in a row.
"The three areas where we had difficulty last year won us the game tonight," said Oilers coach Tom Renney, on his team's power play, penalty-killing and goaltending.
It was first overall draft pick Ryan Nugent-Hopkins' ninth game and he added an assist to sit at nine points on the season.
If he plays a 10th game he will remain with Edmonton for the remainder of the season.
Renney has still not officially announced he is staying, but Nugent-Hopkins was scheduled to take the trip to Colorado for the Oilers' next game on Friday.
For now, Nugent-Hopkins said he was just soaking in his team's effort in knocking off the top team in the league.
"It was awesome," he said. "They were undefeated coming into tonight so to get a win against a good team tonight was great. We really battled hard tonight. Khabibulin, some of the saves he made for us were ridiculous."
Karl Alzner scored for the Capitals, who are one of just 10 teams in NHL history to start a season 7-0.
Washington coach Bruce Boudreau said the Capitals missed their chances to extend their winning streak, largely due to the play of Khabibulin.
"I thought we played pretty good in the third period and came at them," he said.
"Once that first five minutes went by and we didn't get one with the pressure we had on them and on the first power play in the third when (Khabibulin) made that stop on Dennis Wideman, I thought it's going to be hard to score on this guy tonight. We threw everything we could at him."
It didn't help the Capitals' cause that they gave the Oilers eight power plays. Both Edmonton goals came off of the man advantage.
"For whatever reason we took penalties not only in our zone but also in the offensive zone," Capitals goalie Tomas Vokoun said. "Penalties are tough to kill in this league. We had a chance to get a point but they had a bit more puck luck than us.
"You can't take that many penalties, no matter who you are playing. It cost us the game in the end."
The Capitals went up 1-0 at 5:36 of the first as Alzner did a good job to keep a puck in at the point and then wound up and sent a shot past Khabibulin.
Edmonton came close to tying it up on a similar play by Cam Barker, but his shot hit the post behind Vokoun.
The Oilers tied the game at 18:15 of the first period on a nice three-way passing play on a four-on-three man advantage. Eberle slid a quick pass through the crease to Hall, who swatted in his third of the season.
Edmonton took a 2-1 lead at 12:44 of the second with another power-play goal. A big rebound on a Corey Potter point shot came out to Eberle, who put it into the open net.
Washington had a good chance to tie it with four minutes left in the second as Alex Ovechkin picked off a pass in the Edmonton zone for a partial break, but Khabibulin stood his ground to make a kick save.
Khabibulin was strong for the first five minutes of the third, notably making kick saves on Ovechkin and Nicklas Backstrom and robbing Wideman on a slap shot.
Wideman rang another shot off the post on the power play with four minutes left.
The Capitals got another power play in the final minute and pulled Vokoun, but could not get the equalizer.
It was the only meeting between the two teams this season. The last time they played was a 5-0 victory for the Capitals in Washington last season. ... Oilers D Ryan Whitney went for an MRI on his sore right knee Wednesday and the word after the game was that he will likely miss three weeks... Caps D Mike Green has not practiced this week after suffering an ankle injury in Saturday's win over the Wings.
Copyright by STATS LLC and The Associated Press
Arena: Rexall Place Location: Edmonton, Alberta
Referees: Stephane Auger, Dan O'Halloran Linesmen: Michel Cormier, Vaughan Rody
Attendance: 16,839 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Karl Alzner (1)
Assists: Jeff Halpern, Jason Chimera
Taylor Hall (3)
(Power Play) Assists: Jordan Eberle, Corey Potter
Jordan Eberle (2)
(Power Play) Assists: Corey Potter, Ryan Nugent-Hopkins