In November 1962, Scepter Records released her first solo single, "Don't Make Me Over", the title of which Warwick supplied herself when she snapped the phrase at producers Burt Bacharach and Hal David in anger. Warwick had found out that "Make It Easy on Yourself" — a song on which she had recorded the original demo and had wanted to be her first single release — had been given to another artist, Jerry Butler. From the phrase "don't make me over", Bacharach and David created their first top 40 pop hit (No. 21) and a top 5 U.S. R&B hit. Warrick's name was misspelled on the single's label, and she began using the new spelling, "Warwick", both professionally and personally.
After "Don't Make Me Over" hit in 1962, she answered the call of her manager, left school and went on a tour of France, where critics crowned her "Paris' Black Pearl", having been introduced on stage at Paris Olympia that year by Marlene Dietrich.
The two immediate follow-ups to "Don't Make Me Over" — "This Empty Place" (with "B" side "Wishin' and Hopin'" later recorded by Dusty Springfield) and "Make The Music Play" — charted briefly in the top 100. Her fourth single, "Anyone Who Had a Heart", released in November 1963, was Warwick's first top 10 pop hit (No. 8) in the U.S. and an international million seller. This was followed by "Walk On By" in April 1964, another major international hit and million seller that solidified her career. For the rest of the 1960s, Warwick was a fixture on the U.S. and Canadian charts, and much of her output from 1962 to 1971 was written and produced by the Bacharach/David team.
Warwick weathered the British Invasion better than most American artists. Her biggest UK hits were "Walk On By" and "Do You Know the Way to San Jose?" In the UK, a number of Bacharach-David-Warwick songs were recorded by British singers Cilla Black, Sandie Shaw and Dusty Springfield, most notably Black's "Anyone Who Had a Heart" which went to No. 1 in the UK. This upset Warwick, who described feeling insulted when told that in the UK, record company executives wanted her songs recorded by someone else. Warwick met Cilla Black while on tour in Britain. She recalled what she said to her: "I told her that "You're My World" would be my next single in the States. I honestly believe that if I'd sneezed on my next record, then Cilla would have sneezed on hers too. There was no imagination in her recording." Warwick later covered two of Cilla's songs – "You're My World" appeared on Dionne Warwick in Valley of the Dolls, released in 1968 and on the soundtrack to Alfie.