The first incident unfolded in Birmingham during a local derby between Birmingham City and Aston Villa in the second-tier Championship. During a stoppage in play, a Birmingham fan charged onto the field and took a swing at Villa captain Jack Grealish, catching him on the side of his head.
The unidentified intruder quickly was restrained by a security official as Grealish's teammates rushed in to confront him. The fan was led away by police, waving and blowing kisses to his fellow supporters as he was taken off the field. Grealish appeared not to be seriously hurt and appeared to accept apologies and commiserations from Birmingham City players after the incident.
"I was walking into position and then just felt a whack around the side of the face," said Grealish, who went on to score the only goal in Villa's 1-0 win. "Obviously there's rivalry and stuff in football but I don't think there's any place for that."
"We apologize to Jack and all at Aston Villa Football Club," Birmingham said in a statement. "What happened has no place in football or society."
The English Football League said it "condemns the mindless actions" of the man who attacked Grealish.
"It's a situation no player should ever be faced with," the English Football League said in a statement. "In all circumstances the playing surface is for players, not supporters and those playing in the game must be able to do so safe in the knowledge they will not be subjected to this type of behavior.
"Whilst this incident falls within the remit of the Football Association, we will work with all the relevant parties to address the issue of player and match officials safety on the pitch and ensure the appropriate action is taken."
Hours later in London, an Arsenal fan ran onto the field after Pierre-Emerick Aubameyang scored a penalty to provide the final margin in Arsenal's 2-0 Premier League win over Manchester United. As the fan raced toward the celebrating Arsenal players, he pushed United defender Chris Smalling.
The Metropolitan Police said in a statement Sunday evening that the man was in custody on "suspicion of common assault and pitch invasion." Arsenal announced that he would be banned from all of the club's games, home and away.
"We utterly condemn the behavior of the individual who ran onto the pitch and approached Chris Smalling," the club said in a statement. "We would like to apologize to Chris and Manchester United, and are pleased that the individual was apprehended and arrested. We will be working closely with the Metropolitan Police in their investigation."
Arsenal and Manchester United are two of the most successful clubs in the English game, and their rivalry occasionally has spilled over into outright antagonism and hostility. Both clubs were docked points after a 1990 brawl between the two teams, while another bad-tempered match in 2004 led to Arsenal midfielder Cesc Fabregas throwing a piece of postgame pizza at legendary United manager Alex Ferguson.
The rivalry between Birmingham City and Aston Villa has seen more violence between fans, as both clubs have been followed by well-organized groups of hooligans, known as "firms." In 2002, a Birmingham City fan was arrested and later sentenced to four months in prison after he ran onto the field, made an obscene gesture at Villa goalkeeper Peter Enckelman and slapped the player following an own goal.
Precautionary measures already had been taken in an attempt to reduce the risk of violence.
"We kick off on Sunday at 12 o'clock for a reason, to keep the people out of the pubs," Villa manager Dean Smith said. "Security's got to be ready for people coming on to the pitch but then some lunatic goes on trying to make a name for himself."
Birmingham said it would assist investigators and review stadium safety procedures.
"We deplore the behavior of the individual who committed this act and rest assured he will be banned from St. Andrew's for life," the club said. "The club will also support any further punishment this individual may face in the eyes of the law."
The attack followed a number of recent high-profile incidents of crowd trouble north of the border in Scottish football.
In Friday night's 1-1 draw between Rangers and Hibernian, Rangers captain James Tavernier found himself face to face with a Hibernian fan who had jumped out of the home support stand during a game on Friday night. The previous weekend a glass bottle was thrown from the same section of the stadium as Celtic winger Scott Sinclair prepared to take a corner during a game at Hibernian.
The Associated Press contributed to this report.