The teams played out a 0-0 draw in the first leg in Wellington on Saturday and although both sides had chances in a tense match in Lima, Peru were more clinical in front of goal. Russian Federation 2018 will be Peru's first World Cup since 1982 in Spain. "Now we have to keep working and prepare for the finals".
Jefferson Farfan opened the scoring Wednesday in the 27th minute from the edge of the box.
Peruvian players dedicated the win to striker Paolo Guerrero, who was suspended on doping suspicions.
After coaching several South American clubs, Gareca was hired as Peru coach in 2015, tasked with taking a talented side back to the Finals for the first time since 1982.
A still tearful Farfan said after the match that his team had "to endure a lot of nonsense until we got here".
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In 1985, the then striker scored the goal that guaranteed his home nation their place in Mexico, ironically against Peru, the team he managed three decades later. "From the bottom of my heart, this is for you, Paolo, as I had promised", the Lokomotiv Moscow forward said. A total of 32 countries will compete in the 2018 World Cup.
Peru finished fifth in the tough CONMEBOL qualifying, but were too good for Oceania champions New Zealand in the play-off.
In his press conference Peru coach Ricardo Gareca preferred to thank the team's psychologist for the result.
"He was very important for us at this turbulent moment", Gareca said. "All Peruvians should take this Thursday to celebrate as never before".
Peruvian President Pedro Paulo Kuczynski used Twitter to ask for moderation in the festivities on the holiday on Thursday. "Let's celebrate with responsibility".
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By now, Roger looked to have relaxed into the game and closed in on a quick deciding set in just 26 minutes. A bruising first set went in Sock's favour before Zverev took the second easily .