Marcos Alonso and substitute Cesc Fabregas scored either side of Eden Hazard's magnificent solo effort in the 53rd minute as Antonio Conte's men stretched their advantage at the Premier League summit to 12 points.
Olivier Giroud headed a consolation in stoppage time to prevent Chelsea from matching the scoreline they suffered at Emirates Stadium in September, but it did little to temper the jubilation at the final whistle.
"It was fantastic," Chelsea defender Cahill told Sky Sports. "In football you get the opportunity to put things right.
"I remember the feeling after we got off the field at Arsenal and we were determined to put things right. We did just that.
"We're confident playing at home. We knew a win would be vitally important for us against a massive team.
"We practice this formation, we practice our tactics. The manager is very thorough with that. We take that on board and try to deliver.
"We created a lot and could have had more goals but the second goal was a special goal from a special player.
"The next goal was important after half-time and for me that killed the game."
Hazard was deservedly given the man-of-the-match award after his first goal of 2017 arrived in picturebook fashion.
"It is always good to score beautiful goals against a massive team," he told Sky Sports.
"We scored three beautiful goals and we deserved to win this game."
On his stunning strike, Hazard added: "I try this in all games but it is not like this in every game. I know I need to score more goals, so I am happy.
"We created a lot of chances but on the counter-attack we can so better."