Faulk cut it to 2-1 at 3:59 of the second period, one-timing a short pass from Josh Leivo from the left circle.
Aho made it 3-1 at 16:36 after Svechnikov's centering pass went off the right post before Aho jammed it in the net.
"Their first goal was pretty nice, but on the next two we just lost guys in front," Faulk said. "(On Aho's goal), they have 2 there against our 1, and they were able to tap it in. We kind of gave them chances that are just mistakes on our end."
The Blues tested Andersen on the power play early in the third period, but the Carolina goalie made saves against Brayden Schenn, Nikita Alexandrov and Ivan Barbashev.
"I try not to get ahead of myself and really just focus on each situation," Andersen said. "We've been playing really well too, so obviously that helps."
Jarvis scored at 2:25 of the third period for the 4-1 final when Aho forced a turnover against Colton Parayko in front the net and fed Jarvis, who drew Binnington out of position and tucked the puck inside the left post.
"That kind of came out of nowhere," Jarvis said. "Usually, I would just get that and shoot it. I thought, maybe I'll hold onto it. I tried it, and luckily it worked out."