Timo Werner scored and assisted as he ended a 14-game goal drought to help Chelsea to victory over Newcastle in the Premier League at Stamford Bridge.
Werner's cross rebounded out to Olivier Giroud to net Chelsea's opener in the first half, after the France striker replaced the injured Tammy Abraham.
Summer signing Werner then made it 2-0 eight minutes later, scrambling in a flick-on at the back post.
Victory sees Chelsea move back up to fourth place, ahead of West Ham.
The Hammers, who confortably beat Sheffield United earlier on Monday night, are level on points with Chelsea but both sides sit above defending champions Liverpool as competition for Champions League places heats up.
"We knew we had the opportunity to jump into the top four," Tuchel told BBC Sport. "We took this chance and the guys get a well deserved two days off now.
"There was a big gap between us when we started. It's not over. Now we've made it and it's the moment to hang in and keep on showing the hunger we had. We've made this big step today. We have to follow up and not lose any intensity or determination."
The Blues have now picked up 13 points from a possible 15 under the new leadership, winning four successive league matches in a row for the first time since November 2019.
Tuchel described it as "the perfect evening" but admitted Abraham's injury was "serious enough he had to go out and we worry about him".
Meanwhile David Moyes says it "nearly feels uneasy" talking about West Ham's place near the top of the Premier League after the Hammers beat bottom club Sheffield United.
"We've got five games before April and if we make it to there it might start hotting up," said Moyes after a sixth West Ham win in eight league games.
"But it nearly feels uneasy talking like this. The teams around us are top, top teams and we are going to have to play incredibly well to be there.
"But I think we've got another gear or two to what we've shown tonight."
Sheffield United, 14 points from safety with 14 games left, went close to equalising at 1-0 only for Lukasz Fabianski to produce an outstanding save to keep out David McGoldrick's deflected header.
West Ham had been awarded an early penalty when Craig Dawson was fouled by Enda Stevens and referee Simon Hooper pointed to the spot, but after a VAR consultation the decision was overturned.