The No. 1 seed, ranked fourth in the world, excelled throughout the first set of his latest victory before stuttering and growing frustrated throughout the second of his 6-2, 7-6 (9) win.
He is in Eastbourne for the first time in a change of routine for his preparations for Wimbledon, which begins on Monday.
However the momentum he built during the second set of Wednesday's defeat of Canadian Vasek Pospisil was eroded the longer he remained on centre court against Young.
He required only 26 minutes to take the opening set as he served and volleyed with conviction, dropping only three points on his serve and breaking his opponent twice as the American struggled to find a solution.
Remaining relaxed and encouraging the attention of the crowd during the change of ends when Young, 27, required a medical timeout for a lower-back problem, there appeared little likely to stop him playing with the same rhythm.
On the same day his rival Andy Murray's own build-up to SW19 was undermined by a hip injury, Djokovic was enjoying a rare positive in what has been an unexpectedly-disappointing 12 months, but it was thereafter that his frustration grew.
Young, a former Wimbledon junior champion, played with renewed belief, and after holding his own serve, broke that of the decorated 30-year-old to earn a set point on his own serve at 5-4.
Instead of then forcing a third set, he hit a forehand long, allowing Djokovic to break back, rescue another set point in the tie-break and eventually edge it 11-9 on his fourth match point.