Liverpool is two points ahead of Chelsea in the Premier League, while Atletico leads La Liga by three points over Real Madrid following a 2-1 win at Getafe.
A look at the action across Europe's main leagues:
Philippe Coutinho scored in the 78th minute to help Liverpool become the favorite to win the Premier league on a day of remembrance for English soccer.
The Brazilian playmaker pounced on Vincent Kompany's poor clearance to curl home the winner for Liverpool, which is on course for its first championship since 1990.
"That is probably the biggest statement we have made so far," Liverpool's Steven Gerrard said after leaving the field at Anfield to a standing ovation. "That was the longest 90 minutes I have probably played in. It felt like the clock was going backwards."
Liverpool is seven points ahead of third-place City, which has two games in hand. Second-place Chelsea, like Liverpool, has the title in its own hands but needs to beat Liverpool at Anfield on April 27 and win its other four games.
Liverpool struck early with goals by Raheem Sterling and Martin Skrtel in the opening 26 minutes. City rallied in the second half, with David Silva scoring in the 57th and Glen Johnson's own-goal five minutes later.
Before the game, Liverpool fans held up a mosaic spelling out "96 25 years" during a minute's silence to mark the 25th anniversary of the Hillsborough Stadium disaster. In 1989, 96 Liverpool fans were crushed to death during an FA Cup semifinal.
"We live with Hillsborough every day," Liverpool manager Brendan Rodgers said. "The families and the victims are in our thoughts every day," Rodgers said. "It was an inspiration for us, rather than something that held us back."
Hull's 5-3 victory over third-tier Sheffield United in the second FA Cup semifinal, which set up a meeting with Arsenal in the final, was overshadowed by the latest installment in the fight for the league title.
Chelsea stayed in control of its own fate after Demba Ba's goal secured three points in south Wales.
Liverpool is two points clear of Chelsea with four games left but the pair meet at Anfield in two weeks in what is likely to be a defining match in the race for the title.
Ba's winner in the 68th minute — a left-foot strike from the edge of the area — ended Swansea's stubborn resistance, with the hosts forced to play most of the match with 10 men following the 16th-minute dismissal of Chico Flores for two yellow cards.
Diego Costa was injured while scoring Atletico Madrid's second goal in a 2-0 win at 10-man Getafe on Sunday as the team extended its Spanish league lead with five rounds to play but possibly lost its star striker.
Costa slammed into the post while poking in his 26th goal of the season in the 84th minute, hurting his left shin and requiring the stadium's medical crew to carry him off the pitch while he covered his face and muffled his screams.
Defender Diego Godin gave Atletico the lead in the 40th before Getafe's Alexis Ruano was dismissed with a red card in the 66th, with goalkeeper Jordi Codina saving Costa's penalty.
Atletico took advantage of Barcelona's loss on Saturday to open up a three-point lead over Real Madrid with Barcelona another point behind.
Mauro Icardi scored twice to help Inter Milan beat 10-man Sampdoria 4-0 in Serie A on Sunday and boost its hopes of qualifying for the Europa League.
Walter Samuel and Rodrigo Palacio also scored for Inter while Lopez had a penalty saved. Sampdoria played most of the match with 10 men after Eder was shown a second yellow card for his part in a brawl.
Inter remained fifth but was helped by Parma's 1-1 draw at Bologna and Lazio's 4-2 defeat at Napoli. Hellas Verona's slim European hopes diminished as it lost 5-3 at home to Fiorentina.
Also, Chievo Verona beat Livorno 4-2 in a relegation battle, while Torino earned a 2-1 win against Genoa.
Bayer Leverkusen scored the fastest goal of the season on Stefan Kiessling's header 40 seconds after kickoff on Sunday and beat Hertha Berlin 2-1 in the Bundesliga return for its new coach, moving up one place into fourth.
In the late match, Hoffenheim beat Augsburg 2-0 to come within two points of its opponent in eighth place.
Paris Saint-Germain failed to get over the disappointment of its Champions League exit as it lost 1-0 at Lyon in the French league on Sunday.
A wasteful PSG suffered a second straight loss for the first time this season but still tops the league with a 10-point lead over Monaco with just five rounds left. It lost 2-0 to Chelsea on Tuesday.
Lyon midfielder Jordan Ferri scored the winner with a low curling shot in the 31st minute.
Elsewhere, Saint-Etienne lost ground in the race for a Champions League spot by drawing 2-2 at Reims to trail third-place Lille by seven points.
In the Brittany derby, Serge Gakpe fired Nantes to a 1-0 win over Guingamp, helping his team inch closer to safety.