Cup holders Zenit dominated from the start at Moscow's Lokomotiv Stadium, with Brazilian midfielder Mauricio converting from Artur Yusupov's cross in the 22nd minute.
Reigning league champions CSKA struggled and failed to take the few chances that they created, as Zenit won the season's curtain-raiser for the second year in a row.
"My first game in Russia was very tough and very emotional," said Romanian Lucescu, after claiming the 33rd trophy of his career.
"Russia's league is very strong and it was hard to play the league champions.
"But the positive result in the first match will give me a chance to continue my work here calmly.
"Maybe, the Super Cup is not the most prestigious trophy but it's important for the club's image anyway. I'm very pleased with the result of today's match."
CSKA head coach Leonid Slutsky, who led Russia to an embarrassing group-stage exit at Euro 2016 last month, blamed his players' lack of match practice ahead of the new season.
"We started the match really badly today," he said.
"Our defensive players lacked understanding and we created too few chances in attack. It's natural ahead of the start of the season and we still have some time to improve our performance."
CSKA kick off their league title defence with a trip to Anzhi Makhachkala next Saturday, after Zenit host Lokomotiv Moscow earlier that afternoon.