The former Manchester United and Juventus striker -- who turns 34 next week -- is back at his childhood club after a miserable and controversial brief spell with Chinese club Shanghai Shenhua.
Cristian Pavon gave Boca a second-minute lead with Charrua Nandez adding the second just after the hour mark in Saturday's game.
"It's exciting to feel being alive again," Tevez, who was named captain for the match, told Argentine television channel TyC Sports.
"It's an extra motivation for me that people continue to show the same affection. I enjoyed every moment. I don't see myself suffering, I am very happy to be here."
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The win allowed Boca to move to 33 points and increase their lead at the top of the table to six points from San Lorenzo.
Tevez, who earlier played for Boca between 2001-2004 and 2015-2016, arrived back in Argentina after describing his time at Shanghai Shenhua as a "holiday".
"It's fine because I was on holiday for seven months," he joked in an interview with TyC Sports earlier this month.
After Saturday's match, he added: "My family suffered a lot but I'm trying to get ahead and give people joy."
Tevez's remarks on his time in China prompted an outpouring of anger on Chinese social media, with fans of a number of Chinese Super League (CSL) clubs rounding on the man often disparagingly labelled "very homesick boy" in the Asian country.
"After looking at Tevez's interview my heart as a Chinese football fan is again deeply hurt," wrote another on Weibo.
"While we are chasing Tevez like a rat crossing the street, China's (football) managers should also do some good self-reflection."
Tevez scored only four goals in the Chinese league and missed his team's successful Cup final win, while coach Wu Jingui called him "overweight" when he took over in September.
Tevez is hoping to help Boca end their 11-year wait for a seventh Copa Libertadores title when the South American tournament kicks off later this week.