Li had played nine holes in just 29 blows for the second time this season as he carded a brilliant 63 to set the target at nine under at Bernardus Golf.
It seemed for a long time that the Chinese would lead the way after 36 holes but Gouveia made a move with an eagle on the 12th and then produced his big finish to get to double figures after a 66.
Gouveia is looking to re-establish himself on the DP World Tour after regaining his card as he finished second on the European Challenge Tour last season.
The Portuguese topped the Challenge Tour Rankings in 2015 and enjoyed an impressive debut campaign, earning himself a place in the field at the season-ending DP World Tour Championship, Dubai.
A five-time winner on the Challenge Tour, Gouveia is no stranger to being in contention, and is looking for more of the same in Cromvoirt after an impressive opening two days.
“I just played very solid from the beginning," he said. "I holed a few good putts today again, I think that was the key, and kept it in play so when I missed a few shots I was able to recover well.
“Normally I tend to play well with windy conditions and it just suits my game, so far so good.
"You have to put the ball in the right spots off the tee and then you can create some chances, obviously there are going to be some tucked pins and you have to be smart. That is what I learned from last year.
“I made a lot of birdies so far and I think that shows my putting has been good the last couple of days and I hope I can continue into the weekend.”
I made a lot of birdies so far and I think that shows my putting has been good the last couple of days and I hope I can continue into the weekend
Li made a lightning start as birdies from inside ten feet at the tenth and 11th were followed by an eagle from similar range at the par-five next.
An approach to four feet on the 14th put him five under after five and he played another sublime iron shot on the par-three 17th and made a two-putt birdie on the par-five next to turn in 29.
A bogey on the second quelled any hope of a 59 but Li got up and down at the short par-four third, made a two-putt gain on the par-five fourth and then put his tee-shot to 13 feet on the par-three eighth to lead by one.
It looked for almost the entire afternoon that he would not be caught but Gouveia had other ideas.
The 30-year-old took advantage of the fourth despite a ragged tee-shot and while he gave the shot straight back, a long putt on the next kick-started a hat-trick of gains as he turned in 33.
A second dropped shot of the day would come on the 11th but Gouveia bounced back with an eagle from the fringe at the 12th before an approach to 12 feet on the 16th helped put him in a share of the lead.
He then got up and down from the sand at the last for a closing birdie and a one-shot advantage.
Wallace made the most of both the par-fives on the back nine while also hitting smart approaches into the 11th and 14th to turn in 32. A birdie from ten feet on the third was given back on the sixth but he got up and down on the par-five seventh to pick the shot back up after finding sand off the tee.
Meronk birdied the last to join Wallace at eight under after a roller coaster first 14 holes containing six birdies and three bogeys.
In-form Kiwi Ryan Fox, Finn Mikko Korhonen, Italian Guido Migliozzi, Frenchman Victor Perez and England's Jack Senior were at seven under, a shot clear of Swede Alexander Björk, German Marcel Schneider and another Englishman in Jordan Smith.