A 2-1 win - courtesy of Craig Davies' late penalty - was an eighth in 10 games and left Wanderers in the play-off places with four games to play.
Freedman's side were under pressure for much of the game against a City side now 10 points adrift of safety.
He said: "You need different tools to be a successful side and today we showed our battling qualities.
"The race for play-off places is wide open and I see no reason why Bolton Wanderers should not be in the top six come the end of the season.
"We met a Bristol City side fighting for their lives and working very hard for each other. It was never going to be easy.
"But when other people were opening presents on Christmas Day we were training. Now we are reaping the reward of months of hard work."
The winning penalty came after a linesman spotted s foul on David Ngog, and Freedman said: "I've seen the incident again on film and there was definitely a foul on David.
"The linesman did well to spot it and I thought the officials worked well as a team."