Substitute Marcus Rashford scored an injury-time winner as Manchester United beat Hull City 1-0 on Saturday.
Rashford tapped in from close range in the 92nd minute as United matched Chelsea with three wins from three to open the Premier League season.
“I think we did everything to win,” United manager Jose Mourinho told BT Sport.
“I know when you score in minute 90-something we always speak about a bit of luck but I think the reality is that we deserved it.
“In the second half we were so dominant, so intense in our attacking that I always believed the goal would arrive.”
Hull's David Meyler had a chance for a late winner but fired over the bar and visitors United struck moments later.
Wayne Rooney carried the ball along the byline and sent in a pass which the 18-year-old Rashford, making his first appearance of the season, steered home.
"It is disappointing for the players, they have put a serious amount of work in to get to a point where they think they have a result,” Hull caretaker manager Mike Phelan said.
"I am proud of the players. They have put hard work in today without getting anything out of it."
Eden Hazard, Willian and Victor Moses scored as Chelsea comfortably beat Burnley 3-0 to go top of the table over United on goals scored.
"It was a good game and performance and we played good football," Blues manager Antonio Conte said.
"We created a lot of chances and kept a clean sheet.
"That is important because after 13 home games without a clean sheet this helps the confidence and shows the hard work is paying off."
After opening with a loss and draw, champions Leicester got their first win by beating Swansea 2-1.
Jamie Vardy and Wes Morgan put the Foxes up 2-0 before Leroy Fer's consolation.
"We were disappointed with the first game of the season but got a decent draw last week and played well and we just wanted to keep improving,” Vardy said.
"To go two goals up and then hang on at the end, we got what we deserved.”
Arsenal also broke into the win column with a 3-1 victory at Watford.
Santi Cazorla's penalty put the Gunners in front after nine minutes with Alexis Sanchez and Mesut Oezil adding goals before half-time.
Everton stayed unbeaten by defeating Stoke 1-0 after Shay Given's own goal.
Goalkeeper Given pushed Leighton Baines' penalty onto the post but the ball rebounded off his head and in.
Scott Dann's injury-time goal gave Crystal Palace a 1-1 draw with Bournemouth, the first points for both sides.
Danny Rose's goal earned Tottenham a 1-1 draw with Liverpool, while Sunderland and Southampton are still seeking their first wins after drawing 1-1.
Manchester City can match Chelsea and United's perfect start by beating West Ham on Sunday, while West Bromwich Albion host Middlesbrough.