Grier's tip-in somehow squirted through for the tying goal early in the third, and Connolly scored the winner on a power play and iced it with a short-handed goal in Buffalo's 5-3 victory over the Blues on Sunday night.
Grier and Connolly, who each had two goals and an assist. helped the Sabres win for only the third time (3-11-0) this season when trailing after two periods.
Jochen Hecht added a goal for the Sabres, down 3-2 after two periods. Tim Kennedy, Jason Pominville and St. Louis product Chris Butler each had two assists as the Sabres rebounded from a shootout loss Saturday against Ottawa.
"We didn't play well [Saturday] night," Grier said. "I think we all kind of felt anxious coming into the game tonight and the guys battled. I think it took us a while to find our legs, but we battled and hung in there."
Alex Steen scored twice, and Eric Brewer added a goal for St. Louis.
The Blues have dropped two straight after winning three in a row. They fell to 6-12-2 on home ice after losing for only the second time in regulation (12-2-3) when leading after two periods.
"We came out with the mindset of pushing the shot clock and getting pucks to the net, playing in the offensive zone," Blues coach Andy Murray said. "They took advantage of their opportunities. ... Tough to lose."
Connolly's power-play goal gave the Sabres a 4-3 lead 7:22 into the final period. He redirected Butler's feed past Ty Conklin.
"We were able to move the puck and get a wrist shot through," Connolly said. "I was able to get a piece of it and fortunately, it went into the net."
Blues defenseman Erik Johnson was off for holding, a penalty Murray didn't seem pleased to give up.
"We took a tough penalty, gave up a power-play goal," Murray said. "It went by two guys, a shot from the point. ... I have seen the penalty. We need to kill a penalty and we need to score a power play goal, and we didn't."
Connolly iced the game, backhanding home a short-handed goal with 3:14 remaining after getting a feed from Grier.
"Grier beat the guy, spun out and made a great backhand pass to me," Connolly said. "I was able to get in there and get a break and get it up over [Conklin's glove]."
Buffalo's fifth goal came seconds after the Blues' Brad Boyes had the tying goal on his stick, but the puck was on him quickly and he missed out on knocking in a rebound.
"It came out quick," Boyes said. "I'm trying to get what I can on it. I don't know if I'm too tight there or what, but [Saturday] night in Minnesota was kind of the same thing. A rebound comes out and it goes right by me. It happens real quick, but somehow, you've got to get something on it."
Grier picked up his second of the game after a redirection of Kennedy's pass that Conklin appeared to have covered up. However, the puck somehow squirted through 3:15 into the third period to tie it at 3-3.
Conklin said that he put it in himself.
"I went to close my legs to cover the puck and it hit the inside of my knees and just squirted in," Conklin said. "It's just a fluky goal.
"I knew exactly where it was. I was looking at it. I just went to close my legs. ... That probably won't happen again in two years. It was a fluky goal, but it sets a bad tone for the third period."
Steen opened the scoring for the Blues at 10:12 of the first period. He intercepted Craig Rivet's pass along the right boards, skated into the right circle and beat former Blues goalie Patrik Lalime high to the stick side.
The Sabres countered and got the equalizer when Hecht skated around the goal and whipped a low shot past Conklin at 15:52 of the first.
The Sabres grabbed a 2-1 lead when Grier got a cross-ice feed from Kennedy and beat Conklin 7:47 into the second period. The Blues regained the lead on Brewer's 50th career goal, and Steen's second of the game.
Buffalo's last win in St. Louis came on Oct. 1, 1997, a 3-1 victory. ... Sabres C Derek Roy (upper body) missed a game for the first time this season. He is listed as day-to-day. Defensemen Patrick Kaleta (neck) and Butler (ankle) returned to the lineup. ... St. Louis' Keith Tkachuk has 27 points in 24 career games against the Sabres. ... The Blues had a streak of 21 consecutive penalty kills snapped on Connolly's third-period goal. ... Pominville played in his 289th consecutive game. ... Blues LW Paul Kariya (upper-body injury) left after the first period and did not return. He was injured following an elbowing penalty by Kaleta late in the first.