Raonic, from Thornhill, Ont., could have closed out a straight-sets win in less than 90 minutes. Instead, Young claimed a tiebreaker to take the match into a deciding third set.
"There were there I have to do differently and not put myself in that situation," said Raonic, making his Basel debut. "At the end of the day, the most important thing was to win, no matter how."
Vancouver's Vasek Pospisil, semi-finalist a year ago against Roger Federer, fell 6-2, 6-2 in his second round match against fifth-seeded Bulgarian Grigor Dimitrov.
"Grigor played well, I was not myself, it felt similar to last year," Pospisil said. "I'm just burned out mentally.
"It was a tough match, you can't take anything away form him. I've had a heavy schedule. Since March I've been home nine days."
Federer, the tournament's top seed, had to fight back from a set down before beating Denis Istomin 3-6, 6-3, 6-4 to reach the quarter-finals. The Swiss star will face Dimitrov in the next round.
Raonic now stands 45 points behind Andy Murray in the race to next month's eight-man World Tour Finals in London, with the Scot also winning his second-round match in Valencia.
David Ferrer, one spot behind Raonic, also produced a win in Spain as the chase tightens with this week and next at Paris Bercy to play.
"Even if I was counting the points, it's irrelevant as everyone (in the race) is still playing," said Raonic, who served as a non-playing substitute in London a year ago. "There's not a lot I can do about it except to concentrate on my game."
Raonic next plays Belgian David Goffin, who has risen to a 28th ranking with solid play all season. Raonic faced him in 2011 in a Wimbledon match which did not conclude as Goffin retired after losing the first set.
"He's playing great tennis, he tries to move you around with forehand and backhand and he returns well," said Raonic, now 45-16 on the season. "He does it all well.
"I'll have to try and play as much on my terms as possible."
Raonic took an early lead against Young, which held up as he won the opening set in less than half an hour.
But standing two points from the win in the second-set tiebreaker, the 23-year-old committed a pair of errors which led Young back into contention at 5-all.
The American took advantage of a Raonic error to earn a set point, then levelled at a set each when Raonic's forehand went wide.
In the third set, Raonic recovered from a double-fault and an error which sent him to love-30 in the 11th game, holding his nerve for a 6-5 lead. When Young sent that set into a tiebreak, it came down to Raonic to finish off the victory with his 22nd ace.
"I had a lot of tough moments to squeeze through," Raonic said. "In the second set he fought hard and found a way. I had a few lucky breaks overall to win it."
Federer struggled in the opening set, and even walked toward his chair early in the first game before realizing there was still a point to play.
Istomin had taken just a set off Federer in five previous meetings, last year in Basel, but the Uzbekistan player took the lead after breaking in the sixth game.
However, Federer fought back and took a commanding lead in the second set after breaking when Istomin hit a backhand long.
Istomin battled to stay in the match and saved seven break points in the final set before finally succumbing to Federer in the third game and the second-ranked home favourite went on to clinch the match with a love service game.
Eighth-seeded Ivo Karlovic also advanced after coming from a set down to defeat qualifier Kenny De Schepper of France 6-7 (6), 6-4, 6-3 in just under 2 hours.
The Croatian will face Benjamin Becker in the quarter-finals. The German eased through after Mikhail Kukushkin, who had upset Stanislas Wawrinka in the opening round, retired when trailing 6-7 (3), 7-6 (4), 4-0.
Borna Coric set up a quarter-final against childhood idol Rafael Nadal as the 17-year-old Croatian comfortably beat Andrey Golubev 6-4, 6-4.
— With files from The Associated Press