Both Universitario's goals in Saturday's "clasico" at the Estadio Nacional came from free kicks, which were a speciality that marked the 37-year-old Solano's career as a player in Peru, Argentina and England.
Winger Aurelio Saco-Vertiz put Universitario ahead after half an hour when he curled a free kick into the top corner.
After midfielder Paulo Albarracin's equaliser early in the second half, Edison Flores headed the winner from Argentine midfielder Horacio Calcaterra's free kick in the 65th minute.
"Practice is the secret," left winger Saco-Vertiz told reporters.
He said he and Calcaterra had spent extra time on the training ground to practise with Solano, who was called "little master" by Diego Maradona because of his brilliant free kicks when they were team mates at Boca Juniors in the late 1990s.
Peru's two biggest clubs are struggling in the lower reaches of the "Descentralizado" championship standings, both with 27 points from 23 matches after a fraught start to the season due to financial penalties. Universitario were docked three points and Alianza six.
Solano, who took charge of Universitario in June, had helped them win the Peruvian championship as a player in 2009 after a distinguished career in the English Premier League with Newcastle, Aston Villa and West Ham United.
Meanwhile, former Peru striker Franco Navarro replaced Colombian Diego Umana as the coach of Juan Aurich, the reigning Peruvian champions.