Kang will face James Sacheck of Zionsville, Ind., in Friday's quarterfinal match. Sacheck disposed of Will Osborne of Wichita Falls, Texas in 19 holes during Thursday's third round.
Kang, who earned medalist honors at this year's championship, birdied each of his first two holes to take an early lead at 2-up. Texter battled back, however, with a birdie at the par-5 third and after Kang bogeyed the par-5 fifth, the duo was all square.
Texter went 1-up with a birdie at the par-4 sixth but squared the match again when he bogeyed the 11th.
The 16-year-old Kang birdied the 12th and added a birdie at the par-3 13th to go 2-up. Again, Texter climbed back with a birdie at the 14th and pulled even with Kang with a birdie at the 15th.
Texter moved to 1-up with a par at the 16th after Kang bogeyed the par-3. Texter's late lead was short-lived however, and Kang squared the match with a birdie at the 17th.
The match came down to the 18th hole where a bogey by the 17-year-old Texter, who was the medalist at the 2002 event, opened the door for Kang to advance.
'He's a great competitor,' said Texter. 'He hit every clutch shot he had to. He made no mistakes.'
James Lee of Indio, California birdied the first but stumbled with a double-bogey at the second. He settled down and cruised to a 6 and 4 win over Adam Cohan of Wayne, Pennsylvania to advance to the quarterfinals.
Lee will play Brian Harman of Savannah, Georgia, who ousted Randy Lowry, 3 and 2, on Thursday.
Jordan Cox of Redwood City, California defeated Philip Francis, of Scottsdale, Arizona, 5 and 4 to earn a spot in the quarterfinals. Cox will face off against Michael Randle of Austin, Texas, who knocked off Jesse Speirs, 2 and 1.
Webb Simpson of Raleigh, North Carolina beat Clark Klaasen, 2 and 1, to advance. Simpson will meet up with Patton Kizzire, who ousted Seann Harlingten, 1-up, in Friday's quarterfinal.
'It was a tough match,' said Kizzire. 'My opponent never made any mistakes. I kept asking my caddie, 'does this guy miss a shot?' Luckily, I made four birdies and an eagle and just won more holes than he did.'
The Junior Amateur is one of 13 championships conducted annually by the United States Golf Association each year, 10 of which are strictly for amateurs.