The A-League title holders, searching for their first ever home victory in the regional competition, held a comfortable 2-0 lead after making a dominant start to the Group G match at Cbus Super Stadium.
The away side from South Korea fought back from that early deficit to be leading 3-2 late in the contest on the Gold Coast, and Frans Thijssen's men needed a wonderful strike from Devante Clut, the teenager's second goal of the night, to salvage a share of the spoils.
The result leaves Brisbane third in their group, level on four points with the second-placed Bluewings and five behind runaway leaders Beijing Guoan, who boast a 100 percent record from three matches played after dispatching Urawa Reds 2-0 at home on Tuesday night.
The hosts started confidently and kept the ball well in the opening exchanges. They were rewarded in the 12th minute, when a neat passing move produced the opening goal.
Luke Brattan played the ball out wide to Matt McKay, who advanced and fed Andrija Kaluderovic down a channel inside the area. The Serbian cut the ball back for Brandon Borrello and the in-form teenager dispatched a well-taken finish past No Dong-Geon at the goalkeeper's near post.
The Roar doubled their advantage 10 minutes later following another neat display of technical football.
It began when Henrique did well to retain possession on the left wing, before picking out Jack Hingert on the opposite flank. The fullback moved it on to Borrello, who linked up with Clut, trading passes to release the latter into space at the top of the box. Clut matched his fellow 19-year-old's poise in front of goal, powering a firm, low shot beyond the despairing No.
Suwon had barely threatened throughout the first half but they pulled one back against the run of play in the 39th minute.
Luke Brattan gave the ball away after receiving a throw-in and Jong Tae-Se pounced, advancing on goal and feeding Seo Jung-Jin down the visitors' right. Roar goalkeeper Jamie Young got a hand to the forward's firm shot but couldn't prevent it nestling in the back of the net.
Five minutes into the second half and Suwon were level. This time Seo did it all himself, picking up the ball in Roar territory and embarking on a brilliant solo run.
Matt McKay, Shane Stefanutto and Luke DeVere all failed to snuff out the danger, before a brilliant backheel and turn created the space for Seo to fire past Young, completing his brace and levelling the scores at 2-2 in spectacular fashion.
The turnaround was completed by the K-League side with another memorable goal in the 71st minute. Lee Sang-Ho, receiving the ball from Jong, drove forward from midfield and found Santos on the left wing.
A brilliant sequence of one-touch play followed, the Brazilian substitute supplying Yeom Ki-Hun, who in turn delivered a tempting ball into the area. Fittingly Jong, the man who started the move, arrived at the back post to dispatch a superb volley past the helpless Young.
Brisbane responded by producing a wonder-goal of their own eight minutes later, Clut collecting a Dimitri Petratos pass with his back to goal before turning and firing a vicious, dipping strike which appeared to deceive No and fly into the goal with the keeper stranded.
The Queensland side are back in ACL action with a return fixture against Suwon on April 8, in what already appears a likely decider for the runner-up berth behind Beijing Guoan.