The Bruins got Meszaros, 28, from the Philadelphia Flyers for a 2014 third-round draft choice that becomes a second-rounder if the Bruins reach the Eastern Conference finals and he plays in two-thirds of their playoff games. They claimed Potter, 30, from the Edmonton Oilers.
Both have been frequent healthy scratches this season but bring experience to a group of defensemen that includes four players who have been in fewer than 90 NHL games.
''We acquired these two players for depth,'' Bruins general manager Peter Chiarelli said, ''and when I say for depth, I just want to be clear, it doesn't mean that they're just reserves. It means I look at our defensive corps as a whole, and we're just bolstering that corps and we've got a lot of games in a short period of time.''
The Bruins announced the moves two hours after the 3 p.m. EST trade deadline.
Boston had been seeking a veteran defenseman after Dennis Seidenberg suffered a season-ending knee injury on Dec. 27 against Ottawa. They've also been without defenseman Adam McQuaid since he strained his quadriceps on Jan. 19. Without them, Dougie Hamilton, Torey Krug, Matt Bartkowski and Kevin Miller, all 26 or younger, have played regularly. Zdeno Chara and Johnny Boychuk are the other two defensemen among Boston's top six.
Chiarelli said McQuaid would rest for two to three weeks and be re-assessed then.
Meszaros played 38 games this season with five goals and 12 assists. The nine-year veteran's first two seasons with the Flyers were limited by a back injury in 2011-12, Achilles tendon surgery after that season and a shoulder injury in 2012-13.
''It was tough with the injuries, but being healthy this year and not playing was really tough,'' he said. ''Now I feel strong and I feel pretty good. I can skate pretty good and join the rush and obviously have to be good defensively.''
Potter, a six-year veteran, has five assists in 16 games.
''We brought in two guys, two big guys that can ... both move the puck and both push bodies down low,'' Chiarelli said. ''The defense isn't about one player. It's about the group as a whole and how they interact. That's the way our system is. That's the way our coach is. So these guys both are smart players.
''It usually takes some time for the (defensemen) to adapt to our system, new (defensemen) that were brought in. And I expect the same to happen with these two, but it's a good system, it's a system of trust, and I know they can both contribute to the group.''
The Bruins, in second place in the Eastern Conference, have allowed 138 goals this season, second-fewest in the NHL. But their defense has declined since losing Seidenberg and McQuaid.
While Boston made no major moves, one of its chief rivals did. The Montreal Canadiens obtained wing Thomas Vanek and a conditional fifth-round draft pick from the New York Islanders for forward prospect Sebastien Collberg and a conditional 2014 second-rounder. The draft picks will only change hands if Montreal makes the playoffs.
Vanek has 30 goals in 53 games against Boston.
''I know there's been talk about Vanek going to Montreal, and they've strengthened their team. Good for them,'' Chiarelli said. ''It never seems that we're an anointed winner of trade deadline day, and I'm fine with that.''