The last team to come back from a 3-1 deficit and actually win an NBA playoff series was the 2006 Phoenix Suns. They did it in the first round against the seventh seeded and Gasol-less Los Angeles Lakers, back in the days of Amare Stoudemire and Mike D'Antoni.
For those of you who don't remember what happened, let me give you a quick run down. After Shaquille O'Neal left for the Miami Heat in 2004, the Los Angeles Lakers were hopelessly average. They had gotten Phil Jackson back after a year hiatus, but they still couldn't make any headway beyond becoming a first round knockout, especially with their lack of a legitimate big and over-reliance on Kobe Bryant. Meanwhile, the Phoenix Suns were in the middle of their perennial championship challenger phase, being just good enough to contend for the title, but never really being good enough to beat the Dallas Mavericks or the San Antonio Spurs in order to advance to the NBA Finals.
In 2006, the Suns were a solid team, but one that was desperately missing the presence of an injured Amare Stoudemire. They still had their ways of scoring, but, like the Lakers, they lacked a legitimate post threat. While the Suns high-octane offense could carry them to a good regular season record, they weren't formidable in the playoffs because they could be abused down low, even by a center as terrible as Kwame Brown. The Lakers used this to their advantage, slowing the Suns down and forcing them to play a half-court game. This basically leveled the playing field, and opened the door for the Lakers to take a 3-1 series lead.
Below: How the Suns recovered from the 3-1 deficit, and how the Thunder can do the same.
But we're not here to discuss how the Lakers nearly defeated the Suns, or Kobe's amazing shot in Game 4 that nearly sealed it all. What we are here to discuss is how the Suns recovered from that Game 4 loss, and whether the Thunder can accomplish a similar feat.
The 06 Suns do have many differences with the current Thunder. The Suns were an experienced playoff team, and the Thunder are the new kids on the block. The Suns were missing a key player to injury, while the Thunder are fully stocked. Lastly, the Suns were facing a wonky team in the first round of the playoffs, while the Thunder are facing a deadly team in the Conference Finals.
But, before you turn away, let me state how similar the situation of these two teams actually is. Most importantly, for the first five games of the series, the Phoenix Suns had strayed from their calling card, which was their offense. they had let the Lakers lure them into playing a slow, defensive game. While the Suns had great percentages in the box score, their slowed pace basically took away the advantage their offense gave them, and exposed how terrible their defense really was. Similarly, the Thunder have stayed away from their calling card, which is defense. The Mavericks have lured the Thunder into playing a high-scoring series that shows the Thunder's true weakness, which is their lack of consistent offense. When the Thunder play at a high pace, their defense still shows, but it takes away from the advantage their defense gives them, which is stagnation of the current score. If the Thunder can find their calling card, much like the Phoenix Suns did, then they can come back and win this series.