Chelsea youngsters Armando Broja, 19 and Ike Ugbo, 22, came to the rescue of the European champions on Tuesday evening at the Vitality Stadium.
The young strikers, who were both sent out on loan last year, scored second-half goals to give Tuchel’s side a 2-1 win at Dean Court.
Bournemouth took the lead just after the hour mark when new signing Emiliano Marcondes gave the home fans something to cheer in the 66th minute to spark the game into life.
Substitutes Broja and Ugbo showed Abraham the way to score in the six-yard box with two goals inside four minutes.
The Blues equalised in the 72nd minute when Broja controlled a cross from substitute Baba Rahman before finding the back of the net.
And Chelsea were in the lead four minutes later, Ugbo heading in at the near post.
Tammy Abraham missed three gilt-edged chances, two shots and one header from close range, in the first half as the visitors dominated.