The seventh-ranked Japanese star, eliminated in the second round in Monte Carlo last week, broke the Canadian teenager, ranked 31st, in the opening game of the match.
Nishikori then broke again in the fifth and seventh games to take the set.
After Nishikori broke in the fourth game of the second set, Auger-Aliassime began to fight back. The 18-year-old had five break points in the next game, before the fourth seed held.
The Canadian finally broke, to love, in the seventh game but Nishikori broke straight back and served out to win the match.
In the other early match, seventh seeded Russian Daniil Medvedev beat American Mackenzie McDonald 6-3, 6-2.
Results from the Barcelona Open on Thursday (x denotes seeding):
Kei Nishikori (JPN x4) bt Felix Auger-Aliassime (CAN x16) 6-1, 6-3
Daniil Medvedev (RUS x7) bt Mackenzie McDonald (USA) 6-3, 6-2