Arturo Vidal's brace had the home side 2-0 up after 26 minutes, only for Miroslav Klose to halve the deficit two minutes later.
Mirko Vucinic stretched Juve's lead four minutes into the second half, though, before Hernanes was given his marching orders for a second bookable offence just after the hour mark and Tevez sealed the rout 10 minutes from time on Saturday night.
Chiellini was full of praise for Argentina striker Tevez, who hit the bar from the edge of the box before adding his name to the scoresheet, and also for fellow defender Leonardo Bonucci for his hand in two goals.
"Carlos is a world-class champion, and as well as his goals he is tireless in tracking back to help the team elsewhere," the 29-year-old Italy international said on www.juventus.it. "His foray into midfield on 91 minutes, to go and recoup the ball was worth as much as a goal.
"As far as Leo's concerned, technically speaking, he's right up there with the best in the world. We try our best to give him the best possible opportunity to dictate play from the back."
Chiellini felt the Bianconeri's ability to swiftly restore their two-goal cushion after Klose's strike was key to the success.
"We lost a bit of our togetherness after the second goal and allowed (Antonio) Candreva and Hernanes too many shots. We can't commit errors like that, because those two players are the key to Lazio's strength, other than Klose's ability in front of goal.
"After half-time, we regrouped as a team and showed a different attitude, and Hernanes' sending-off left Lazio with little chance of making a comeback."