Super Mario Bros.: Peach Hime Kyushutsu Dai Sakusen!

Super Mario Bros. The Great Mission to Rescue Princess Peach Japanese , Hepburn Sp Mario Burazzu Pchihime Kyshutsu Dai Sakusen? is a 1986 anime film based on the Super Mario Bros. video game. Directed by Masami Hata and produced by Masakatsu Suzuki and Tsunemasa Hatano, the plot centers on Mario and Luigi, who get stuck in a Family Computer video game and must save Princess Peach from Bowser. It is notable for being the first movie based on a video game, predating the liveaction Super Mario Bros. movie by seven years.

The film opens with Mario playing his Family Computer. Suddenly, Mario witnesses a girl on the TV screen crying for help from the enemies attacking her and escapes by jumping out of the TV. After the enemies left, the girl reveals herself as Princess Peach. Just then, Bowser appears and jumps out of the TV. Despite Marios battling attempts, Bowser successfully captures Peach, and takes her back into the TV. Shortly afterwards, Mario discovers a small necklace that Peach left on the floor.The next day while he and Luigi are working at a grocery store, they realize the necklace that Peach dropped becomes a matter of concern for Mario. Luigi then regards it as the Visionary Jewel from the Country of Treasure. Soon, Kibidango, a small doglike entity, wanders into the store and snatches the necklace from Mario, prompting he and Luigi to pursue him into the Mushroom Kingdom. ........

Source: Wikipedia