Celtic opens gap at top of Scottish Premiership
However, the Hoops came out revitalised in the second half as Kyogo Furuhashi and Nicolas Kuhn scored twice in five minutes to put them 2-0 up on the hour mark.
Adam Idah scored twice, netting on either side of Musa Drammeh's consolation, with his second coming from the penalty spot in the 94th minute.
After Aberdeen's first loss of the season earlier in the day, Celtic gave itself some breathing space at the top of the league, while also moving 11 points clear of firece rival Rangers, which sits third.
"I'm really pleased. Tynecastle is a really tough place so to win 4-1 was really pleasing," Rodgers said.
"Second half, we figured out their press. They have normally been pressing in 4-4-2 but changed it slightly. It just meant we had to drop a man in our build-up play.
"We had some good moments in the first half, but once we were able to play through that pressure, I thought in the second half we were excellent.
"It's a very exciting period for us. All the players know they will play, they just need to be ready."