Deanna Nolan had 20 points, grabbed a career-high 11 rebounds and handed out six assists for Detroit, who take a 2-1 lead in the best-of-five series.
Game Four is on Thursday in Phoenix.
The Shock led by six points entering the fourth quarter before holding off a furious rally by the Mercury, who cut their deficit to 79-77 on two free throws by Kelly Miller with 2:15 remaining.
However, Smith, who connected on 8-of-15 from the floor, found Nolan in the right corner for a deep three-pointer that increased Detroit's advantage to 82-77 with 1:53 left.
After Cappie Pondexter split a pair of free throws with 29 seconds remaining to cut the Shock's lead to 82-79, she missed a shot from the arc with 21 ticks on the clock.
It was the 11th consecutive miss by the Mercury, who misfired on their last 13 shots of the contest.
Smith was fouled and made both of her shots from the charity stripe to make it 84-79 with 20 seconds remaining.
After Tangela Smith and Miller each made one of two free throws to again cut Phoenix's deficit to three, Cheryl Ford stole a pass from Tangela Smith off an offensive rebound.
Nolan was fouled with eight seconds left, making both free throws to push the lead to 86-81.
Miller made two more from the free throw line to get the Mercury within one possession of a potential tie, but Nolan nailed two more foul shots with 4.2 seconds left to seal the victory.
Nolan and Smith combined to make 6-of-6 free throws in the last 20 seconds.
Reserves Plenette Pierson and Shannon Johnson scored 12 and 11 points respectively for Detroit, who shot 44 percent (34-of-78) and won their first road game of the play-offs.
Diana Taurasi scored 22 points and Tangela Smith had 17 points and 12 rebounds for Phoenix, who suffered their first home play-off loss in 2007.
Penny Taylor had 16 points and a career-high 14 rebounds and Pondexter added 13 points for the Mercury, who shot just 35 percent (25-of-72) after connecting on 42 percent or better in the first two games of this series.