"Drive" was The Cars' highest charting single in the United States, peaking at number three on the Billboard Hot 100 chart. On the Adult Contemporary chart, the song went to number one. It reached number four in West Germany and number six in Canada. In the UK "Drive" reached number five in October 1984 on its initial release, but following its use at the Live Aid concert in July 1985 as the background music to a montage of clips depicting the contemporaneous Ethiopian famine, the song was re-released and peaked at number four in August 1985. Proceeds from the sales of the re-released song raised nearly £160,000 for the Band Aid Trust: Ocasek presented the charity's trustee Midge Ure with a cheque for the amount while he was in London in November 1986 promoting his solo album This Side of Paradise.
In a retrospective review of the single, AllMusic journalist Donald A. Guarisco praised the song for being "a gorgeous ballad that matches heartfelt songwriting to an alluring electronic soundscape. The music reflects the lyrical tone with a lovely melody that rises and falls in a soothing yet sad fashion."
The music video was directed by actor Timothy Hutton and features model and actress Paulina Porizkova, who would later become Ric Ocasek's wife. The video alternates between shots of Orr sitting in a disused nightclub, facing mannequins posed at the bar as customers and bartender, and scenes that depict the breakdown of a relationship between the characters played by Ocasek and Porizkova. Ultimately left alone, the woman cries and laughs hysterically for a time before visiting the nightclub. She looks sadly in through a dirty window at the stage, where tuxedo-clad mannequins of the band members are posed with their instruments as if playing a show, and turns to walk away as the video ends.