Chelsea trailed to visiting Hull but Didier Drogba hit his second goal of the game in the 90th minute to secure a 2-1 victory, while City won 2-0 at Blackburn through goals by Emmanuel Adebayor and Stephen Ireland.
But Arsenal produced the performance of the day by dominating Everton 6-1 at Goodison Park to equal the biggest opening away win in the Premier League's 17-year history.
"It's a good win, but come on, let's face it, we're not going to win 6-1 every day," said Arsenal captain Cesc Fabregas, who scored twice. "It's just one more game for the title race.
"We can do it if we play like that."
The Gunners produced slick, attacking football to dismantle last season's fifth-place team, contrasting with a win for Chelsea that owed much to luck.
Drogba's winning goal came from an attempted cross that floated over goalkeeper Boaz Myhill and in at the far post from an acute angle.
"I was trying for a cross," Drogba said. "It was difficult but it's always good to win the first game. The belief is strong, as always. Today, we showed we will try till the end of the game.
"We were lucky to score, but the desire is always there."
The win gave Chelsea an early lift in its attempt to clinch the league for the first time since 2006 and end Manchester United's record-equaling run of three straight titles.
The defending champion hosts Birmingham on Sunday, when last season's runner-up Liverpool is at Tottenham. Arsenal, which could also be a strong contender this season, was at Everton later Saturday.
Manchester City has spent almost 100 million pounds ($166 million) on new players since the end of last season and one of its new recruits put the club 1-0 up in the third minute of his debut.
Adebayor, signed from Arsenal for 25 million pounds, took a pass by Shaun Wright-Phillips and smashed the ball into the net from the edge of the area.
Blackburn had chances to equalize but Ireland made the game safe for City, which has not won any trophies since 1976, when he calmly placed the ball past goalkeeper Paul Robinson in the last minute.
It was the first time in a year that City's defense held out an opposition attack away from home.
Arsenal's performance against the FA Cup runners-up hinted that manager Arsene Wenger may have been wise when he refused to disrupt his team of young players by spending the proceeds of Adebayor's sale on big-name stars.
Denilson hit a fierce shot from outside the area for 1-0, Thomas Vermaelen headed in on his debut and William Gallas made it 3-0 before halftime when he headed in Fabregas' free kick.
Fabregas then struck twice in the second half and substitute Eduardo da Silva added the sixth to hand Everton its worst ever home loss in the Premier League. Louis Saha got Everton's only goal in injury time.
The five-goal margin matched Bolton's 5-0 win at Leicester in 2001 and Liverpool's 6-1 win at Crystal Palace in 1994.
Aston Villa finished sixth last season but was jeered from the field by its fans after a 2-0 loss to visiting Wigan. Hugo Rodallega put Wigan ahead in the 31st when he volleyed in a dropping ball from the corner of the area and Jason Koumas struck 11 minutes into the second half with his first goal from open play in two years with the club.
"It's a very good start," Wigan manager Roberto Martinez said after his first Premier League game. "Any win in the Premier League is a difficult one and it's down to the players. They were brave on the ball against a top club."
Fulham did not win in its first 14 away games last season, nor in the first 17 away games the year before, but opened with a 1-0 victory at Portsmouth on Saturday.
Bobby Zamora, who scored just two goals in 35 Premier League games last season, scored the winning goal in the 13th minute against a team that has sold many of its best players to reduce its debt.
Sunderland's Darren Bent scored in the fifth minute of his debut to give his new team a 1-0 win at Bolton, while Stoke beat Burnley 2-0 in the visitors' first topflight match since 1976.
West Ham beat the other promoted team, Wolverhampton Wanderers, 2-0 at Mollineux through goals by Mark Noble and Matthew Upson.
The second-tier League Championship opened last weekend and Coventry made it two wins from two games by beating Barnsley 2-0. Promotion favorite West Bromwich Albion profited from an own-goal to win 1-0 at Nottingham Forest, while Shola Ameobi hit a hat trick as Newcastle beat Reading 3-0 to continue its unbeaten start.
