The Gunners kicked off at the London Stadium knowing Chelsea had moved six points ahead of them following their 3-1 victory at Manchester City.
But Arsenal responded in the best possible style as a second-half Alexis Sanchez hat-trick fired them up to second.
"It became a kind of must-win game for us when Chelsea won and obviously the gap opened to six points," goalkeeper Cech told the club website.
"We knew what we had to do and we did it in a very professional way, so we are happy.
"We a lot of opportunities in the first half but it wouldn't go in. In the second half at 1-0 their keeper made some fantastic saves and you think it could still be a dangerous scoreline.
"I know a lot of people would have been a bit anxious, but we showed the maturity not to panic and we kept going. We thoroughly deserved the goals for our performance."
