The 18-year-old looked unbeatable on serve as he eased past Gulbis in straight sets to continue an impressive season in which he has shot to 21st in the world rankings.
"I was surprised because I thought it would be a lot tougher," he said. "I still have a lot to learn on grass."
Fellow Canadian Milos Raonic marked his return with a hard-fought win over Australian teenager Alexei Popyrin, having missed the entire clay season with a knee injury.
The 28-year-old survived an early scare to win 6-7 (6/8), 6-4, 7-6 (7/4) and set up a second round meeting with Jo-Wilfried Tsonga.
Tsonga's fellow French veteran Gael Monfils also advanced to the second round on Tuesday after a gutsy win over American Steve Johnson. The Frenchman was a break down in the final set, but fought back to win 7-5, 5-7, 7-6 (8/6).
After rain delays and two German defeats the day before, the crowd in Stuttgart had home wins to cheer on Tuesday as Jan-Lennard Struff beat Canada's Denis Shapovalov and qualifier Dustin Brown surprised Australia's John Millman.
Brown now faces fellow German Alexander Zverev in the second round on Wednesday.
Elsewhere, Hungary's Marton Fucsovics eased past Spain's Jaume Munar in straight sets, while the USA's Denis Kudla and Italy's Matteo Berrettini made equally light work of their first round matches against Croatia's Viktor Galovic and Australian Nick Kyrgios.
Frenchman Lucas Pouille edged Feliciano Lopez in a third-set tie-break, while his compatriot Gilles Simon came from behind to beat German Peter Gojowczyk.
Results from the ATP tournament in Stuttgart on Tuesday (x denotes seeding):
Gael Monfils (FRA x5) bt Steve Johnson (USA) 7-5, 5-7, 7-6 (8/6)
Gilles Simon (FRA) bt Peter Gojowczyk (GER) 4-6, 6-2, 6-3
Matteo Berrettini (ITA) bt Nick Kyrgios (AUS) 6-3, 6-4
Denis Kudla (USA) bt Viktor Galovic (CRO) 6-3, 6-2
Lucas Pouille (FRA) bt Feliciano Lopez (ESP) 6-3, 3-6, 7-6 (9/7)
Dustin Brown (GER) bt John Millman (AUS) 6-4, 7-6 (7/3)
Felix Auger-Aliassime (CAN x7) bt Ernests Gulbis (LAT) 7-5, 6-3
Jan-Lennard Struff (GER) bt Denis Shapovalov (CAN x8) 7-5, 6-4
Marton Fucsovics (HUN) bt Jaume Munar (ESP) 7-6 (7/5), 6-4
Milos Raonic (CAN x6) bt Alexei Popyrin (AUS) 6-7 (6/8), 6-4, 7-6 (7/4)