Quarterback Tommy Grady threw seven touchdown passes against Chicago, but he was intercepted four times by the Rush's opportunistic defense.
"I thought we played with good energy at the beginning of the game and solved some of our third-quarter issues," James said. "… We were better. But better isn't good enough."
Down 56-48 with less than two minutes left, Grady hit Brandon Thompkins with a 45-yard touchdown pass. A two-point conversion tied the game.
Chicago recovered the onside kick, however, and held the ball until Martinez's winning field goal.
"The defense played a little stronger," James said. "We got the pass rush going a little more, and the secondary showed some resiliency. But we missed some opportunities to score. You can't afford to squander that in a back-and-forth game."
Utah jumped to a 7-0 lead when, on its first offensive play of the game, Grady hit Aaron Lesue for a touchdown.
After Chicago tied the game, Utah struggled on its second possession and faced a fourth-and-2 at the 23. But Grady rolled right and found Thompkins in the end zone to put the Blaze back in front, 14-7.
Another Grady-to-Lesue touchdown pass enabled Utah to take a 28-21 lead into the final 1:54 seconds of the half, when it appeared the Blaze defense made a stop. But an offside penalty negated an interception, and Chicago tied the game at halftime.
It was 35-35 midway through the third quarter when Chicago's Jorrick Calvin intercepted Grady and put the Rush in position to take control of the game. Instead, Utah defensive lineman Keenan Mace stuffed an option play on fourth down from the 2-yard line and the Blaze regained possession.
Grady quickly drove Utah down the field for a touchdown, but Adrian Trevino missed the extra point and the Blaze owned a precarious 41-35 lead.
Chicago followed with two touchdowns the second when Grady's arm was hit and linebacker Kelvin Morris returned the interception for a touchdown that made it 58-46.
Rush 59, Blaze 56
O Chicago's Jose Martinez kicks a 23-yard field goal as time expires to give the Rush a 59-56 win over Utah.
• The Blaze lead most of the way but end up suffering their third consecutive defeat.