The Russian couple sealed an 8-4 victory over the Norwegian pair of Kristin Skaslien and Magnus Nedregotten, scoring a point in each of the last three ends.
"It's very important that we are family," Bryzgalova said. "That was very important in order to survive yesterday's (semi-final) loss.
"Just to come out here today and to make the match that we can be proud about. The fact that we are family helped us a lot."
Canada face world champions Switzerland later on Tuesday to decide the gold.
Married last year, Krushelnitckiy and Bryzgalova have been the darlings of the mixed doubles competition which is making its debut as an Olympic event at the Pyeongchang Games.
The teams play a maximum eight ends as opposed to 10, and there is no shot-calling skip as in the four-player, single sex format of the sport.
The Russian pair have played a daring and entertaining brand of curling and it cost them in their semi-final against Switzerland when Krushelnitckiy's last rock shot sailed through the house to end their hopes of taking on Canada in the final.
The 2016 world champions quickly put the disappointment behind them, storming to 5-2 lead after four ends against the Norwegians and never trailed.
"When we came here, we didn't have any special feelings," Krushelnitckiy said. "We were absolutely calm.
"Then we had the first match and we lost.
"We didn't feel the ice. We didn't feel anything. After that we came back step-by-step to the bronze medal match. And we can be proud about the whole tournament and all the matches."
(Editing by Greg Stutchbury and Ed Osmond)
