Madison Square Garden was electric on Tuesday night. The seats vibrated to chants for Carmelo Anthony and the bellowing applause for J.R. Smith, who had just been named the NBA’s sixth Man of the Year. The players started the game with a ton of energy, and the fans remained on their feet for the entire game.

The New York Knicks won their second game of the postseason, jumping out to a 2-0 series lead over the Boston Celtics, one of basketball’s perennial contenders. The victory marks the first time since 2000 that the Knicks have won more than one game in a playoff series. New York’s recent performance is a reassuring sign of the franchise’s turnaround. Fans have been longing for this playoff success for at least a decade.

In the past few seasons, the Knicks’ defense was laughable, and the offense hinged its hopes on open 3-pointers and streaky shooting.

This year, gears have shifted within the organization. Excuses have become apologies, coupled with admissions of failure and guarantees for future improvement. Defense has become a priority, and the potent offense is balanced with multiple scoring threats and selfless facilitators.

While the Knicks are fueled by a desire to meet their hometown’s lofty expectations, the Celtics have been struggling. Their big three — Ray Allen, Kevin Garnett and Paul Pierce — were broken up when Allen left to play for the title-defending Miami Heat. Rajon Rondo has been sidelined with a torn anterior cruciate ligament. The Celtics limped into the playoffs as the seventh seed.

Then something terrible happened. The Boston Marathon bombing left the entire city in shambles. In an instant, one of America’s most powerful metropolises had its identity maimed by a horrific act of terror.

In their recovery, Bostonians have turned to their enduring sports teams for solace and stability. The Celtics, who had been struggling to find a sense of purpose until recently, are now playing for something greater than a championship. The Celtics are playing for every person in Boston, knowing full well what success on a national stage could do for their city at a time like this.

The next two games of the series will be played in Boston, and while the Knicks will look to continue their success and win their first playoff series in 13 years, the Celtics will be feeding off a different motivation.

Whatever the results of the series, expect the next two games to be far more intense.