The Cardinals (5-8) snapped a six-game losing streak by handing the Lions (3-10) their fifth straight defeat in a most frustrating fashion.
Plummer threw a pass that Claiborne returned 38 yards deep into Arizona territory. But the play was wiped out by offsetting penalties and Plummer made the most of his second chance. The oft-maligned quarterback completed a 23-yard pass to Kevin Kasper, setting up the game-winning kick by Gramatica.
Gramatica had sent the game into overtime with a 41-yard field goal with 3:23 left in the fourth quarter.
"I was very shocked on the call the official made on the interception," Porcher said. "The call changed the whole momentum of the game. We were in field goal range to win the game and the call came back on us. That was the hand that was dealt and we have to live with that."
The Lions have lost 15 straight games on the road.
"We have four games left in the season and we are not going to roll over and die for anyone," Lions quarterback Joey Harrington said. "The official made the call against us and there is nothing you can do but keep on playing."
Plummer completed 24 of 43 passes for 228 yards and was not intercepted.
Eddie Drummond of Detroit opened the scoring with a 73-yard punt return just 1:45 into the contest.
The Cardinals answered with a seven-play, 76-yard drive that ended with a one-yard touchdown pass from Plummer to fullback Joel Mackovica. Marcel Shipp had consecutive runs of 13 and 16 yards that put the ball at the one.
The Lions regained the lead at 14-7 on a six-yard touchdown pass from rookie Joey Harrington to Mikhael Ricks with five seconds left in the opening period. Harrington was 20 of 37 for 152 yards.
Cornerback Todd Lyght helped the Lions increase the lead to 10 points, intercepting Harrington and returning the ball 31 yards to the Arizona 19, setting up a 26-yard field goal by Jason Hanson.
Plummer cut the Lions' halftime lead to 17-14 with a 10-yard pass to Nathan Poole.
The only scores of the third quarter were field goals of 20 yards by Hanson and 29 yards by Gramatica.
The Lions settled for their third-quarter field goal after a blunder by running back James Stewart. On second and goal, Stewart collided with teammate Ray Brown and fell to the ground without being touched by a Cardinal. Thinking he was down, Stewart flung the ball in frustration instead of getting up and going into the end zone.
After a review, the play was ruled an incomplete pass and the Lions soon settled for a field goal.
Stewart gained 52 yards on 13 carries.