South Korea were booed off the pitch in Seoul after a goalless draw against Palestine last week but rebounded with a 3-1 win in Muscat to move into second place in Asian qualifying Group B behind Jordan.
Tottenham Hotspur forward Son said he had talked to his teammates about putting their false start behind them in the five days between the two qualifiers.
"I tried to lead by example," Son said in televised comments reported by Yonhap news agency.
"Some players feel the pressure of being on the national team. Obviously, we should all hold ourselves accountable but I also told the guys that they don't have to hang their heads because we had played just one match.
"We have eight matches to go and that means we have eight more opportunities to play our best. If we can play with confidence like we did today, I believe we will be in good shape."
Hwang Hee-chan gave the South Koreans a good start with a goal in the 10th minute at the Sultan Qaboos Sports Complex but that was cancelled out just before halftime when defender Jung Seung-hyun headed the ball into his own net.
Son put South Korea ahead again by curling a left-foot shot just inside the post from the edge of the box in the 82nd minute and Joo Min-kyu put the victory beyond doubt with a strike deep into stoppage time.
"We didn't get off to such a great start," Son added. "But after winning this difficult away match, I feel like we've become a better team."A top-two finish in Group B will secure direct passage to the 48-team finals in the United States, Mexico and Canada.
South Korea next face a trip to Jordan on Oct. 10 and Son hoped the playing surface at Seoul World Cup Stadium would be in better condition than it was last week by the time they host Iraq in the capital five days later.
"The field was in such excellent shape that we played with confidence," Son said of the Muscat pitch.
"I hope conditions at our home stadium will continue to improve.
"We'll try to play the best match of our lives every time we go out."
