Liverpool cranked up the pressure on West Ham United manager Slaven Bilic with a 4-1 victory at the London Stadium, while Burnley's remarkable start to the Premier League season continued thanks to a 1-0 victory at Southampton on Saturday.
A stoppage-time goal from Martin de Roon earned Middlesbrough an unlikely 1-1 draw at Premier League leaders Manchester City on Saturday.
Captain Steven Gerrard scored twice to rescue Liverpool from FA Cup embarrassment and lead them into the fourth round after a tricky 2-1 win at fourth tier AFC Wimbledon on Monday.
A controversial last-gasp goal deflected into the net off Laurent Koscielny's hand from a close-range shot by Alex Oxlade-Chamberlain gave Arsenal a lucky 1-0 victory at Burnley on Sunday as manager Arsene Wenger marked his 20th anniversary at the club.
Here are five talking points from the weekend's action:
Southampton's rich vein of form in the Premier League continued as they beat Burnley 3-1 with two goals from Charlie Austin on Sunday while another promoted side, Middlesbrough, fared just as poorly, losing 1-0 at home to Watford.
Liverpool were sent spinning to a 2-0 defeat at promoted Burnley in the English Premier League on Saturday while Chelsea came from behind to win 2-1 at Watford thanks to late goals from Michy Batshuayi and Diego Costa.
Wales enjoyed their greatest day in football for more than half a century by overwhelming Russia 3-0 in Toulouse on Monday to win Group B at Euro 2016 ahead of their oldest rivals England.
Wales's Euro 2016 victory over Belgium, officially the second-best team in football, showed again that you can have all the attacking talent in the world but if you are weak at the back you will be found out at the highest level.
Rampant Wales defeated Belgium 3-1 to reach the Euro 2016 semi-finals with a victory that included a sensational strike by Hal Robson-Kanu and a goal for captain Ashley Williams on Friday.
Middlesbrough are back in the Premier League after a 1-1 draw with 10-man Brighton & Hove Albion in their multi-million pound promotion decider on Saturday while Burnley sealed the Championship title with a 3-0 victory at Charlton Athletic.
Mourinho's tinkerings meant a first start of the season for midfielder Scott McTominay, playing on the right of a three-man defence, while Anthony Martial played instead of the dropped Alexis Sanchez. On this evidence, more changes may be needed when United take on Valencia in the Champions League on Tuesday.
Manchester United spurned a chance to move into the Premier League's top four after striker Zlatan Ibrahimovic missed a penalty in a 1-1 draw against 10-man Bournemouth on Saturday.
Images from the English Premier League matches played on Sunday
Ecstatic Wales coach Chris Coleman praised his "soldiers" after a shock 3-1 win over Belgium at Euro 2016 took the country to their first major tournament semi-final, and said they could match anyone if they were not afraid to fail.
Wales outplayed Russia 3-0, scoring twice in the opening 20 minutes, as they moved into the round of 16 at Euro 2016 by winning Group B on Monday.
Images from the English Premier League matches played across England on Tuesday
Northern Ireland set a record of 10 games unbeaten with a 1-0 win over Slovenia after a goal by Conor Washington in a friendly on Monday in the build-up to their first European Championship.
News of all that's transpired on and off the football field
Wales reached the Euro 2016 quarter-finals with a 1-0 win over Northern Ireland thanks to an own goal by Gareth McAuley in a poor encounter at the Parc des Princes on Saturday. Centre back McAuley turned a Gareth Bale cross into his own net 15 minutes from time in the all British last-16 clash.
Wales will move higher than their richer rivals and neighbours England when the new FIFA rankings are announced after Euro 2016, the first sign for what, many predict, will be a bright future after they made history at the tournament. Playing in their first finals since 1958, the Welsh reached the last four of a major tournament for the first time and are expected to move up close to the top 10 countries in the world rankings.
Images from the English Premier League matches played on Saturday
News of all that's transpired on and off the football field
France substitute Kylian Mbappe engineered two late goals to rescue a 2-2 draw against Iceland and spare the blushes of the world champions in their friendly.
News of all that's transpired on and off the football field
Manchester United stretched their unbeaten run to 11 games in all competitions after Daley Blind, in-form striker Zlatan Ibrahimovic and substitute Henrik Mkhitaryan gave them a 3-1 home win over Sunderland on Monday. Left back Blind fired United ahead with a crisp 39th-minute shot after Ibrahimovic teed him up perfectly. The towering Swede doubled the lead with a clinical 82nd-minute finish for his 17th goal of the season. Fit-again Mkhitaryan put the icing on the cake with a spectacular backheel effort after a sharp Ibrahimovic cross from the right, although television replays suggested the Armenian was marginally offside. Striker Fabio Borini gave Sunderland fans something to cheer with a dipping late volley.
Tottenham Hotspur's tenacious chase of leaders Chelsea continued as they claimed a 12th consecutive Premier League home win with a 4-0 rout of Bournemouth on Saturday to cut the gap to four points.
Spain started their World Cup qualifying campaign with a crushing 8-0 win over Liechtenstein, laying down a marker in Group G with a ruthless second-half display on Monday.