Connolly has five points in two games after signing a two-year, $9 million contract extension Wednesday. Lalime, who has stopped all but two of 69 shots in the past two games, improved to 2-2-1 after taking over for Miller, who is out indefinitely because of a high left ankle sprain.
"Ryan's a top goalie in this league and I told him the last five months I've been taking a lot of notes watching him play," Lalime said. "I'm trying to have some fun and do my job."
Playing against the team he has had the most success against in his 10-year career, Lalime moved to 8-2-1 lifetime against the Coyotes after entering with a sparkling 1.64 goals-against average. Lalime blanked the Coyotes in his last meeting with them last season, and had a shutout streak of 129 minutes, 44 seconds against them snapped when Matthew Lombardi scored in the third period.
"I didn't know about those stats," Lalime said. "I don't know. Sometimes you just feel good about a team."
Lalime's best stop came early in the second period when he denied Phoenix forward Viktor Tikhonov's attempt from 5 feet out on a backdoor play with the Sabres up 2-0.
"He gave us a lot of momentum with some saves," Buffalo coach Lindy Ruff said.
Connolly, meanwhile, is more relaxed after being the source of trade speculation leading up to Wednesday's trade deadline. The center tied a career high with four points, and logged almost 20 minutes of ice, the most of any Sabres forward.
"You try not to think about it, but obviously those [rumors] can creep into the back of your head," Connolly said. "The biggest thing is we now have our team set and we can focus on the last stretch here."
Defenseman Andrej Sekera added a goal and assist, and Jason Pominville and Drew Stafford also scored for the Sabres, tied with Carolina for ninth place in the Eastern Conference -- one point behind Florida, the New York Rangers and Pittsburgh.
Buffalo won for the first time at home against Phoenix since Jan. 1997 -- a stretch of eight games -- and beat the Coyotes by a combined score of 7-1 in two meetings this season.
After a sluggish first 5 minutes, the Sabres scored on two of their first three shots on Phoenix goalie Ilya Bryzgalov, who was making his sixth straight start.
Bryzgalov finished with 26 saves for slumping Phoenix, losers of four of the last five and 13 of its last 17.
"We started really well and had some chances," Coyotes coach Wayne Gretzky said. "We got back into it at 3-1, but kind of came up short."
With 84 seconds to go, the Sabres tried to get Connolly his third goal by stacking their lineup with four forwards with the Coyotes short-handed. The move caused both teams to bark at each other at the red line after the final buzzer.
"We understand Connolly has two goals and they want to go for the hat trick, but we don't understand using four forwards with a D-man when it's a 5-1 game with a minute to go," Coyotes captain Shane Doan said. "That's disrespectful to the other team, and it causes some emotion."
Connolly got things going for the Sabres 7 minutes into the game when he deflected Jaroslav Spacek's shot from the point while standing to the right of Bryzgalov along the edge of the crease.
Sekera made it 2-0 just 78 seconds later, and Connolly notched his 13th of the season on the power play with 5:43 to go in the second period.
Lombardi, obtained from Calgary on Wednesday in the Olli Jokinen deal, made it 3-1 7 minutes into the third period before Pominville and Stafford capped the scoring with a power-play goals during a 37-second span with under 3 minutes to go.
The Coyotes will continue their five-game trip Sunday at the New York Islanders. ... After scoring 12 goals in the first 58 games, Buffalo defensemen have tallied five times in the past seven games. ... RW Maxim Afinogenov was shaken up and went to the locker room after a hard hit into the end boards by Phoenix D Ken Klee in the second period, but was able to return. ... There were no penalties called in the first period, but 24 minutes worth of infractions in the second. ... The Sabres have won nine of their last 12 at home.