Frank Lampard opened the scoring with his second penalty in two matches after 18 minutes, but to their credit the Royals stormed back to take the lead at the break through Pavel Pogrebnyak and Danny Guthrie strikes.
However, the Blues managed to get back into contention with a Gary Cahill effort on 69 minutes, before Fernando Torres and Branislav Ivanovic sealed victory for the Stamford Bridge side.
Roberto Di Matteo was pleased with the efforts of his team and glad to get three more points.
“It was a very entertaining game for the supporters. I was very pleased with how we started but then we lost a bit of our composure,” he told Sky Sports.
“In the second half we wanted to keep them under pressure and we did so. We had to take a bit of a risk but we managed to get the goals and win the game.”
By Gareth McKnight