Wenger pumped his fists in delight at the final whistle, as a season that has brought so much criticism for the 67-year-old ended in Wembley glory with a record 13th FA Cup win for the Gunners - and a record seventh for the Frenchman.
The Premier League champions also claimed Sanchez handled in the build-up. And their task became even harder when Victor Moses was rightly sent off by Taylor in the second half after receiving a second yellow card for diving.
After only four minutes, Alexis Sanchez handed Arsenal the lead in contentious fashion, when referee Anthony Taylor overruled his assistant after he had flagged for offside against Aaron Ramsey.
Diego Costa revived Chelsea's hopes of a repeat of their league and FA Cup double in 2010 when Arsenal keeper David Ospina failed to keep out his deflected shot with 14 minutes left.
Arsenal, outstanding throughout, refused to be denied and were back in front inside three minutes when Ramsey, who scored the FA Cup final winner against Hull City in 2014, did it again with a header from substitute Olivier Giroud's cross.
They had one mindset, to walk off as winners, and that was clear to see. They played the better football and wanted it more. The Chelsea players were hanging their heads but they had an unbelievable season. On the day, not enough players turned up, they did not deserve to win.
Arsene Wenger was right when he said the season has been a tough one for the players and fans, but they turned up today.
Arsenal defender Rob Holding had a fantastic semi-final too and he was under the spotlight, as was Per Mertesacker. Both players put on a huge display. What a performance Mesut Ozil put in too. Man for man, Arsenal fared much better than Chelsea.
Chelsea looked like amateurs playing next to Arsenal in this round. The Premier League champions could not handle Arsenal's footballing ability in the middle of the pitch. They could not get any rhythm or get on the ball. It was Arsenal's best display of the season.