The Shock were on the verge of ending a season-high three-game losing streak with a 58-48 cushion with 14:52 remaining. But the Lynx responded with 17 of the next 21 points, highlighted by eight from Hayden.
Amanda Lassiter forged a 62-62 tie with a jumper at 10:22 and Hayden gave Minnesota the lead for good with a runner 45 seconds later.
Detroit was within 75-70 after Merlakia Jones made a jumper with 82 seconds left, but Swin Cash committed an offensive foul on the next possession for the Shock and Smith made three free throws in the final 24 seconds.
Jones finished with 16 points and Deanna Nolan, Cheryl Ford and Cash each had 13 for the Shock.