Both goals came in first-half stoppage time, from Mason Mount and then Olivier Giroud, the latter after Pulisic fed Mount, who found the Frenchman.
Pulisic finished his first Premier League campaign with nine goals and six assists in 25 matches.
His 2019-20 season is not over, however. He will go for his second cup trophy -- he won the German Cup with Borussia Dortmund when he was a second-half sub in 2017 final against Eintracht Frankfurt -- when Chelsea faces Arsenal in Saturday's FA Cup final at Wembley.
After that, Chelsea travels to Bayern Munich a week later for the second leg of their Champions League round-of-16 series, more than five months after it fell to Bayern, 3-0, at home.
The 2020-21 Premier League will start on Sept. 12.