"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.
On the Hot R&B/Hip-Hop Songs, it reached a peak position of number 31.
The New York Times editor Stephen Holden described this ballad as a "booming generic ballad to which Houston applies her typical stentorian delivery."
Allmusic's Stephen Thomas Erlewine praised the song as "first-rate urban pop song that skillfully captures Houston at her best."