"Run to You" was written by Jud Friedman () and Allan Rich. Originally intended to be a break-up song, it was approved by the production and stars. However, a month later, the director of The Bodyguard (Mick Jackson) called, saying he liked the song so much, but he'd rather have it to be a love song so the entire song was rewritten, except for the title.

All of the previous releases from The Bodyguard had been successes, landing in the top five. "Run to You" became a moderate hit, peaking at number 31 on the Billboard Hot 100. In the US, it spent six weeks inside the top 40, five of which were spent at the number 31 peak. Airplay and singles sales topped out at number 26 and 41, respectively. The single sales stalled at number 41 on the Hot 100 Singles Sales chart, most likely due to the fact its parent album, The Bodyguard, already was certified 8× platinum and nearing 9× platinum status quickly. Single sales were moderate because most consumers already owned the song by simply owning the album.

On other Billboard charts, the song was moderately well received. On the Hot R&B/Hip-Hop Songs, it reached a peak position of number 31. The song cracked the top 10 on the Hot Adult Contemporary Tracks chart, peaking at number 10.

Internationally, it was not as well received, except in the UK and Ireland, peaking at number 15 and number 9, respectively.

"Run to You" and its soundtrack-mate "I Have Nothing" were nominated for a 1992 Academy Award for Best Original Song, but they lost to "A Whole New World" from Aladdin.

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