The 31-year old Nishikori, a semifinalist in Rotterdam two years ago, beat the Canadian for the second time in as many meetings and will face either Alex de Minaur or John Millman in the second round.
Seventh seed bows out as Nishikori ends four-match losing streak
Nishikori's serve was under pressure early on, taken to deuce in the second game and having to save a break point in the fourth, but he hung on both times to level the set at 2-2.
Later in the set, it was Auger-Aliassime who saw his serve threatened, stretched to deuce a couple of times, but a combination of big serves and Nishikori errors saw the Canadian through.
The set would eventually go a tiebreaker with Nishikori gaining an immediate mini-break before the seventh seed was back on serve at 4-3. The Japanese quickly regained his advantage and clinched the set after Auger-Aliassime chipped a backhand wide.
After getting treatment on a knee injury suffered late in the tiebreaker following the first game of the second set, Auger-Aliassime was severely compromised and Nishikori took full advantage, cruising through the second set.