The song's music video, directed by Colin Tilley, was released on June 2, 2016. As of September 2020, the music video has accumulated over 187 million views, making it his most viewed video on his Vevo channel.
In the US, on the Billboard chart dated June 4, 2016, "That Part" made a debut at number 92 on the chart. The following week, the single completely fell off of the chart, however, on the chart dated July 2, the song re-entered at a new peak of number 76, due to the announcement and anticipation of his then-upcoming album Blank Face LP. In the following weeks, the song climbed up, eventually reaching a new peak of number 40, becoming his second top 40 hit as a lead artist and fourth overall, and his second highest position behind 2014's "Studio", which peaked at number 38, two years earlier. The record has thus charted for 13 weeks by far for the date ending September 17. In New Zealand, the single failed to crack the top 40, however, it peaked at number six on the Heatseekers chart, making it his first appearance as a lead artist in that country with the debut coming from the release and chart debut of his sophomore album with another song titled "By Any Means", also charting in the same chart at number eight.