United was already under regular pressure before Wan-Bissaka's rash challenge on Christopher Martins deep in the Young Boys half.
Young Boys deservedly leveled in the 66th when midfielder Nicolas Moumi Ngamaleu met a low cross into a crowded goalmouth with a shot that beat goalkeeper David de Gea at his near post.
It proved to be another tough Swiss trip for United after losing in the group stage at Basel twice in the past decade.
Ronaldo claimed a share of more Champions League history just by playing his first United game in the competition since the 2009 final. His 177th career appearance in the Champions League tied the record held by Iker Casillas, his longtime teammate at Real Madrid.
The Champions League qualifying rounds seemed to have prepared Young Boys well for facing a star-studded United team playing just its fifth competitive game of the season.
The Swiss team was sharp and physical in its 13th game of a season that started in mid-July with the first of six Champions League qualifiers.
Also in Group F on Tuesday, Villarreal was hosting Atalanta in a later kickoff.
United hosts Villarreal on Sept. 29 — a rematch of last season's Europa League final the Spanish club won. Atalanta hosts Young Boys on the same date.