Tuchel told BT Sport: "We played a good away game, excellent result, a good mixture. We created a lot of half chances, we were a bit unlucky with offsides but I am happy if we create. We need to be strong from first to last minute, it was a deserved win.
"Very good first half, we struggled with decisions and precision in the last third and could have created more chances. At two goals, anything can happen and the stadium can wake up but we did not allow them into the game and finished them off."
Hosts Leicester brought in Daniel Amartey and Marc Albrighton to replace injured pair Youri Tielemans and Ricardo Pereira from the side that drew 1-1 at Leeds before the international break. Chelsea, meanwhile, had Mason Mount back following dental surgery, with Trevoh Chalobah coming in for Andreas Christensen. Pulisic was fit enough for the bench following his return from injury and he made a scoring return to action after he came on in the second half.
Ben Chilwell, booed on his return to the King Power, should have opened the scoring against his former side on four minutes but blasted his shot against the bar from inside the area, much to the home fans' relief. Chilwell was smiling moments later, though, as his corner kick from the right found Rudiger, who rose highest to glance a header past Kasper Schmeichel for his second goal of the campaign.
Just before the half hour mark, another former Leicester man played a starring role in Chelsea's second. Kante, who won the title with Leicester in 2016, stormed through midfield unopposed and his left-footed strike beat Schmeichel to double his side's lead.
Rodgers, forced to bat away speculation linking him with Manchester United on the eve of the match, cut a frustrated figure in the first half with Ademola Lookman's effort disallowed for offside the home side's only notable threat on the Chelsea goal.
Chilwell brought a fine save out of Schmeichel early in the second half as Chelsea threatened another, before Tuchel brought Pulisic on for his first appearance since Nov. 6. The United States international wasted little time in getting involved and slotted past Schmeichel for Chelsea's third with 20 minutes to go.
The goal capped a fine week for the 23-year-old, who scored in USMNT's 2-0 win over Mexico last Saturday before featuring in the midweek draw with Jamaica. Pulisic thought he had added his second and Chelsea's fourth with 10 minutes to go but he was marginally offside.
Tuchel praised Pulisic's play, saying afterward: "One of his key qualities is to arrive in the box and, more importantly, the six-yard box. This is a top quality and we need this. He gives something, of course, in terms of repetitive sprints, intensity on and off the ball, but he is hungry to score and arrives in the box. This is where we need players."
It wasn't all smiles for the leaders, though, as Jorginho limped off with what looked a hamstring injury late on. By that point, many of the home supporters had seen enough and made their way to the exits.