With just five minutes remaining and still trailing to Eidur Gudjohnsen's penalty, the Reds dug deep to equalise through Raheem Sterling before Philippe Coutinho scored the winner in added time.
Bolton played the final 25 minutes with 10 men after Neil Dann's sending off but defended resiliently until their late collapse.
"We have got a great habit at the minute which is winning games," said Rodgers.
"You can't question the character. They have shown a real strong mentality in my time here.
"At 1-0 I expected us to win it. The confidence at the moment is very high.
"Our composure after the penalty - it was never a penalty - was very good. We scored two and could have had many more."
Coutinho signed a new five-year contract this week and marked the occasion with a dipping shot for only his third goal of the season.
The Brazil international has arguably been Liverpool's best player in their resurgence over the last two months and Rodgers believes the 22-year-old can reach even greater heights.
"You would pay money to watch the kid," he added.
"He is a great role model for lots of technical players in this country. He will become world class in the next couple of years.
"Luis Suarez grew and grew in this team and I can see Coutinho falling in the same way, although he might not be as prolific.
"Signing a new deal shows he is really committed to Liverpool and his development."
Source: PA