The 6-0 start is Detroit's best ever and extends the Shock's winning streak to eight games dating to last season's WNBA Finals.
Shannon Johnson added 12 points and Swin Cash had 11.
Asjha Jones scored 20 points and Lindsay Whalen 19 to lead Connecticut.
The Sun (4-3) trailed by as many as 15 and were down 71-64 with just over four minutes remaining. But Connecticut reeled off the next seven points, tying the game on a Katie Douglas layup with 2:43 left.
A pair of Cash free throws put the Shock back up 73-71. After a defensive stop, Smith hit a 3-pointer as the shot clock expired with 32 seconds to go. The teams traded free throws the rest of the way.
The Shock and Sun combined for 52 fouls in a physical game. There were also three technicals.
The Shock jumped out to a 10-2 lead to open the game, holding Connecticut to 1-of-9 shooting.
The Sun cut the lead to three before going cold again, and Detroit led 28-13 at the end of the quarter.
Connecticut came back in the second quarter, cutting the deficit to six at 32-26 when Whalen found Jones for a fast break layup with 4:07 remaining. A Deanna Nolan jumper just before the halftime buzzer put the Shock up 37-30.
Connecticut's 7-foot-2 center, Margo Dydek, finished with 11 points, including a 3-pointer. She also had nine rebounds and two blocked shots.
Detroit leads 16-13 in the all-time regular season series between the two teams, who meet again Friday in Detroit.
