Produced by Mattman & Robin and Shellback, "Run Away with Me" is a dance-pop and synth-pop tune with an upbeat production containing a distorted, reverbed saxophone riff.

"Run Away with Me" was accompanied by a DIY music video filmed by Jepsen's then-partner David Kalani Larkins in Paris, Tokyo and New York City, which also premiered in July 2015.

Spin magazine referred to "Run Away with Me" as "the best pop song of 2015 yet", "an undeniable hit waiting in the wings for its moment", and a "big, bold, beautiful masterpiece".

[13] Pitchfork ranked it at number 36 on their 200 best songs of the decade list, saying that "fueled by a yearning saxophone riff and colossal drums, Jepsen gleefully repeats her heartfelt invitation until the rest of the world melts away.

"Over the weekend, we could turn the world to gold," she murmurs with a quiet devotion, letting the image of two gilded lovers linger in the air.

"[7] Variety's Rachel Seo named it Jepsen's best song in October 2022, writing that its "galloping beat and soaring chorus is the stuff of every coming-of-age swan song for those whose bildungsromane were written, or re-written, during the [2010s], joining the array of tracks — like Lorde's 'Green Light' or Taylor Swift's 'Style' — that have emerged as frontrunners of music written to express something profound about growing up and falling hard.

[29] The clip pictures the singer in the Place de la République, Place Charles de Gaulle and on the Eiffel Tower in Paris, in Shibuya Crossing and a karaoke bar in Tokyo, and in New York City where she is seen running along the fountain in Columbus Circle and pointing at the Statue of Liberty from a boat in New York Bay.