Peru secured fifth spot in the 10-team South American zone's final standings with a 1-1 home draw against Colombia on Tuesday, guaranteeing an intercontinental playoff against New Zealand, reports Xinhua news agency.
The teams will play a two-legged home and away tie in November for a berth in football's premier event in Russia next year.
"The message I have to supporters is that they shouldn't stop believing. Be confident and keep faith in us," Gareca told reporters.
"To be in this position was one of our targets for the qualifiers. There's 180 minutes left. We know that it is difficult but we know that it is up to us."
If Peru qualify, it would represent a curious twist of fate for Gareca. It was the Argentine who killed off Peru's hopes of earning a place in the 1986 World Cup with his late goal in a decisive qualifier in Buenos Aires.
Peru has clearly forgiven the 59-year-old, who has overseen a stark change of fortunes for the national team.
Having looked destined to miss the World Cup after a 2-1 loss to Chile in Santiago a year ago, Peru are now one of the region's most in-form sides and are unbeaten in their past six matches.
They have also had their share of luck. Earlier this year they were aided by a FIFA decision to strip Bolivia of their 2-0 victory over the Blanquirroja in La Paz for fielding an ineligible player. The three points awarded to Peru proved pivotal in CONMEBOL's final standings.
The optimism surrounding the Andean nation's qualifying hopes was shared by President Pedro Pablo Kuczynski, who took to social media to thank Gareca and his players while rallying Peruvians to get behind the team.
"Guys, thanks for the happiness, we are still in the race," he wrote. "Now let's prepare because success is guaranteed. Let's go Peru!"
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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