Kevin Johnson added 16 points, including two baskets in an 11-0 run that put the Golden Hurricane (26-11) up 59-40 with 9:28 to play.
After nearly blowing a 20-point lead and a pair of 18-point advantages earlier in the tournament, Tulsa led Alabama (25-11) by at least eight points for the final 24:36 to win its second NIT title.
The previous championship came 20 years ago, when the Golden Hurricane beat Syracuse 86-84 in overtime in Nolan Richardson's first year as coach.
Peterson, tied Richardson's school record for wins in his first year.
Greg Harrington scored 11 points and Charlie Davis added a season-high 10 for the Golden Hurricane.
Tulsa used its superior quickness to frustrate Alabama, deflecting passes and pressuring the ball constantly.
The Tide shot only 33 percent for the game compared to 53 percent for the Golden Hurricane.
The Golden Hurricane held Alabama's leading scorer, Rod Grizzard, scoreless for the first 33 minutes. Grizzard had his shot blocked when he went inside and threw up airballs from 3-point range.
Erwin Dudley scored 17 points and Terrance Meade added 14 to lead the Crimson Tide, who went to the NIT final with five sophomore starters and last year's high school player of the year in reserve.
Tulsa broke out to a 14-point lead in the first half behind runs of 11-2 and 15-3. The Tide went nearly seven minutes at one stretch with only one field goal and trailed 36-25 at the half.
But that didn't soothe Peterson, who screamed at Jason Parker when the guard took a wild shot with 20 seconds left in the half. ``Get over here! What are you doing? I told you to hold for the last shot!'' Peterson yelled.
That was about all that went wrong for the Golden Hurricane, who added an NIT title to their three trips to the NCAA round of 16 in the past eight years.
In the consolation game, Memphis beat Detroit 86-71.