All three Dallas shooters beat Turco to the stick side and the Stars ended their season-worst four-game winless streak (0-3-1).
Jonathan Toews beat Stars goaltender Kari Lehtonen in the first round to match Morrow's goal, but Richards scored in the second round and Lehtonen denied Patrick Sharp's second-round bid.
Ribeiro was mobbed by teammates after his third-round goal clinched the extra point.
Morrow notched the tying goal 47 seconds into the final period when he batted the puck out of the air and past Turco. Morrow appeared to score with a high stick, but after a video review, the goal stood.
Stephane Robidas and Richards scored second-period goals for the Stars, who had been 1-5-1 in their previous seven. Turco made 32 saves in his first game against his former team, and teammate Patrick Kane had a goal and two assists.
Turco played for Dallas for nine seasons before becoming a free agent in the offseason. The Stars opted to go with Kari Lehtonen as their No. 1 goaltender, and Turco signed with Chicago.
Turco is currently the backup to rookie Corey Crawford, but coach Joel Quenneville gave Turco the start against his ex-teammates in the first game of a back-to-back.
Kane triggered his team's three-goal first-period flurry as Chicago scored on three of its first five shots against Lehtonen.
Brent Seabrook and Sharp also scored for Chicago, and Toews added two assists for the defending Stanley Cup champions.
Kane intercepted an up-the-middle breakout pass by Dallas defensemen Nicklas Grossman and beat Lehtonen from the slot at 3:39 of the first period.
It took only 21 seconds before Seabrook's goal from almost the same spot as Kane's tally made it 2-0. Grossman's turnover in the corner led to the score.
The Hawks bumped their lead to 3-0 at 12:56 of the first period when Sharp converted Toews' centering pass on the power play for his team-high 28th goal of the season.
Chicago nearly made it 4-0 during a 5-on-3 advantage with less than 5 minutes remaining in the first period. Seabrook shot from the right circle, Lehtonen made a flashy glove save near the goal line, and a video review proved inconclusive as to whether the puck crossed the line.
Turco had a stress-free first period, having to make five easy saves, but the Stars stepped up the pressure with a 17-shot second period.
Robidas' goal at 15:59 of the second ended Turco's bid for his 42nd career shutout, and Richards' power-play goal with 4.2 seconds left in the second made it a one-goal game.
Blackhawks right wing Fernando Pisani left the game with a head injury and did not return. With 14:31 left in the second period, Pisani was knocked into the Dallas bench on a hard check by Dallas defenseman Mark Fistric.
Pisani's head struck the edge of the bench and he was down for several minutes before being helped to the Chicago locker room.
Fistric received a double-minor for roughing and interference.
The Blackhawks also announced in the third period that center Ryan Johnson and left wing Viktor Stalberg would miss the rest of the game with injuries sustained in the first two periods.
Notes: The Stars ran a brief tribute to Turco on the main scoreboard during a break in the first period. A large portion of the crowd stood and applauded Turco, who played 259 games for the Stars in their current home arena. ... The Stars are without C Adam Burish (broken orbital bone), RW Krys Barch (scratched cornea and fractured orbital bone), RW Ray Sawada (separated shoulder and broken nose), C Jamie Benn (shoulder) and C Toby Petersen (leg). ... RW Michael Frolik made his debut for the Blackhawks after being acquired in a trade with Florida on Wednesday. ... Chicago RW Marian Hossa missed the game with the flu.