Aaron Ramsey scored a brace as Wales won 2-0 against Hungary while a Serge Gnabry hat-trick powered Germany to a 6-1 win against Northern Ireland.
Aaron Ramsey has agreed to make a lucrative switch to Italian champion Juventus when his Arsenal contract expires at the end of the season.
Arsenal saw off highly-fancied Napoli 2-0 at the Emirates, while Marco Alonso's late header earned Chelsea a hard-fought win at Slavia Prague.
Arsenal climbed two points above fourth-placed Tottenham and fifth-placed Manchester United to bolster their chance of qualifying for the Champions League.
Aaron Ramsey is already free to sign a pre-contract agreement with foreign clubs.
Arsenal turned on the style against Fulham, recording their biggest win of the season.
Arsenal quickly ended any doubt over the contest on the field as Aaron Ramsey and Alexandre Lacazette both scored twice in the first half to surely put the tie out of CKSA's reach.
Pierre-Emerick Aubameyang's lively debut was aided by three assists from Henrikh Mkhitaryan in his first Arsenal start.
It was Arsenal's third FA Cup win in four seasons and 13th in total.
Strikes from Aaron Ramsey, Neil Taylor and Gareth Bale overwhelmed Russia in Toulouse as Wales comprehensively won the match 3-0 to enter the Round of 16 of Euro 2016.
Olivier Giroud's second goal put Arsenal F.C., attempting to move closer to their first title since 2004, 3-2 ahead but Liverpool F.C.'s Joe Allen left them frustrated with his last-gasp equaliser.
Manchester United F.C. rode on Wayne Rooney's lone goal to defeat Sheffield United in FA Cup, while defending champions Arsenal and Manchester City beat Sunderland and Norwich City respectively to enter the fourth round
Olivier Giroud and Aaron Ramsey were on target for Arsenal as they moved on top of the English Premier League table.
Aaron Ramsey limped off in the second half of Arsenal F.C.'s Champions League win over FC Bayern Munich on Tuesday and a scan on Thursday revealed he is unlikely to be back in action for several weeks.
Wales had qualified for their first major tournament in 57 years on Saturday when they lost 2-0 away to Bosnia-Herzegovina but Cyprus's 2-1 win in Israel guaranteed them a place in the top two in Group B.
Arsenal thought they had gone ahead when Aaron Ramsey finished off a glorious through ball from Santi Cazorla. The linesman though thought otherwise.
Aaron Ramsey has been heavily linked with a possible move to Barcelona this summer but the Welshman quashed such rumours saying his sole focus is to beat Aston Villa at the Wembley Stadium and defend their FA cup title.
Goals from Olivier Giroud, Aaron Ramsey and substitute Mathieu Flamini ensured Arsene Wenger's side will travel to Monaco brimming with confidence.