Weekes made 12 of his saves after the first period as Carolina held on for its fifth win in the 10 games since Laviolette took over for fired coach Paul Maurice.
"It's mind-boggling that we have to sweat that out 2-0 at the end, but at least we were sweating it out and it wasn't 0-2," Laviolette said. "We've still got a ways to go, we still have to get better at a lot of different things. When we do, i think we'll just keep improving."
Weekes' fifth shutout of the season helped the Hurricanes snap a three-game losing streak.
Markov gave the Hurricanes the lead 5:07 in with an assist from Adams, who stretched the advantage to 2-0 at 7:03 of the first by scoring a short-handed goal.
The teams went scoreless the rest of the way.
"I thought we had pretty good energy from the first shift," Adams said. "We were keyed up. You kind of have to have that mentality of desperation. ... We're at the point where we can't be letting points slide."
In the second period, St. Louis managed 10 shots but couldn't beat Weekes. Chris Osgood made 22 saves for St. Louis.
"I felt good," Osgood said. "They did a good job of driving the net, and it gave me trouble. I thought they played well. They are a good defensive team that's been having trouble scoring."
St. Louis coach Joel Quenneville said his club was outmatched in this game.
"It looked like the strength on the puck and the energy levels were at two different levels, and they had a lot more of it," Quenneville said. "You could tell on the first goal, the puck's there, they beat us to the front of the net, it's in our net."
Blues forward Keith Tkachuk left the game toward the end of the second period because of a sore neck.
Carolina has two goals in its last 46 power-play chances and none in four games. ... The Hurricanes, with 36 points, are four behind their pace of last season. ... St. Louis is 2-6 in the second game of back-to-back sets. ... St. Louis was 6-0-1 in its previous seven games against the Hurricanes, including three straight wins overall and three in a row in Carolina.
Copyright by STATS LLC and The Associated Press
Arena: PNC Arena Location: Raleigh, North Carolina
Referees: Don Koharski, Jay Sharrers Linesmen: Steve Miller, Mark Shewchyk
Attendance: 8,865 (47.3% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Danny Markov (4)
Assists: Marty Murray, Kevyn Adams
Kevyn Adams (4)
(Shorthanded) Assists: Sean Hill, Bret Hedican