The Russian prevailed 7-5, 4-6, 6-7(6), 6-1, 6-4 in a contest that lasted 3 hours and 50 minutes, ending Tien's impressive run at Flushing Meadows.
The victory sends Khachanov into his first US Open quarter-final since 2022, when he reached the semi-finals in New York. He will now face Belgian Alexander Blockx for a place in the last four.
Tien fights back after losing opening set
Khachanov made the stronger start, taking the opening set 7-5 after converting his opportunities at crucial moments.
Tien, however, responded impressively. The 20-year-old American levelled the match by taking the second set 6-4, before producing another strong performance in the third.
The third set went to a tie-break, where Tien held his nerve to win 8-6, moving to within one set of the biggest Grand Slam victory of his young career.
But Khachanov refused to let the opportunity slip away.
Khachanov turns the match around
The experienced Russian raised his level dramatically in the fourth set.
Khachanov dominated the set 6-1, putting immediate pressure on Tien's serve and forcing the American into increasingly difficult positions.
The momentum had completely shifted by the deciding set.
Khachanov secured the crucial break and maintained his composure through the closing stages before sealing victory 6-4 in the fifth set.
The statistics underline the quality of the contest. Khachanov hit nine aces and won nine of 12 break points, while Tien converted five of 14 opportunities.
Tien's breakthrough run ends
Despite the defeat, Tien can look back on a significant breakthrough at this year's US Open.
Before this tournament, the American had never won a main-draw match at the US Open in three previous appearances. His run to the fourth round therefore represented a major step forward in his Grand Slam career.
Tien has also enjoyed a remarkable rise in the rankings over the past two years, moving from around world No. 232 to the top 15.
His defeat means he narrowly misses out on another milestone — becoming one of the American men through to the US Open quarter-finals.
Khachanov continues resurgence
For Khachanov, the victory represents another important step in his resurgence at Flushing Meadows.
The Russian, who reached the 2022 US Open semi-finals, had failed to progress beyond the second round in his following three appearances at the tournament. He has now returned to the quarter-finals after overcoming Tien in one of the most competitive matches of the fourth round.
Khachanov's next challenge will be Alexander Blockx, who reached his first Grand Slam quarter-final after defeating 24th seed Francisco Cerúndolo 6-3, 4-6, 7-5, 7-5.
Karen Khachanov 3-2 Learner Tien — Match result
• First set: Khachanov 7-5 Tien
• Second set: Khachanov 4-6 Tien
• Third set: Khachanov 6-7(6) Tien
• Fourth set: Khachanov 6-1 Tien
• Fifth set: Khachanov 6-4 Tien
Final score: Karen Khachanov 7-5, 4-6, 6-7(6), 6-1, 6-4 Learner Tien
Khachanov's comeback ensures the Russian remains in contention for his first Grand Slam final, while Tien leaves New York with one of the most encouraging performances of his developing career.