With 2,000 home fans in attendance at Stamford Bridge, following the rollout of new COVID-19 tier rules in the United Kingdom, Leeds took a shock early lead through Patrick Bamford, but the home side gradually found their stride and, after missing several chances, the net.
A frenetic opening continued at the other end when Bamford gave Leeds the lead in the fourth minute, with the former Chelsea forward beating home keeper Edouard Mendy to Kalvin Phillips' long through ball and slotting into an empty net.
The hosts looked certain to equalise five minutes later, but Timo Werner somehow contrived not only to block Giroud's goalbound header, but then hit the cross bar from inches away. Giroud, retained in the line-up after his four-goal game at Sevilla in midweek, then shot wide after seizing upon an errant Meslier clearance.
Finally, though, the Chelsea pressure told. After Ziyech played him on the right side, Reece James sent in a low cross that Giroud expertly converted with a low, left-foot volley for his first league goal of the season.
Ziyech appeared to suffer an injury in the build-up to the goal and his immediate exit saw the introduction of U.S. international Pulisic from the substitutes' bench.
Giroud has been urged by France coach Didier Deschamps to play more top-flight football before next year's European Championship, raising speculation he might leave Chelsea in January if he cannot get more game time.
"I feel good and confident. I play with serenity. I had the opportunity to score again today and help the team," Giroud said after the match.
After a quiet start to the second half, Chelsea took the lead on the hour mark. Meslier made a fine double save from Werner and Ezgjan Alioski deflected a Mason Mount shot over, but Leeds' set-piece vulnerabilities were in evidence again from the corner that followed.
Mount's service from the right was headed in powerfully by Zouma, who registered his fourth league goal of the season. Leeds complained of a Giroud foul, but referee Kevin Friend awarded the goal as home fans celebrated.
In the closing stages, Werner was denied by Meslier again and substitute Tammy Abraham shot wide before Pulisic converted from close range in stoppage time to claim his first league goal of the season.
With the goal, Pulisic becomes the fastest American to score 10 goals in the Premier League, having needed just 30 games. Clint Dempsey (57), Brian McBride (36) and Roy Wegerle (14) are the only other U.S. players to reach double figures for goals.
Leeds, back in the top flight after 16 years, looked dangerous on the break in the first half, pouncing on any Chelsea error to flood forward before fading.
"I was nervous of Leeds," Lampard said. "They're a threat until the end if you don't get a cushion. On another day we could score five or six and finish the game but we are still developing and being more clinical is in that."