SAN FRANCISCO — As a top executive at Google for the past 13 years, Marissa Mayer played an instrumental role in developing many of the services that have tormented Yahoo as its appeal waned among Web surfers, advertisers and investors.

Now, Yahoo is turning to its longtime nemesis to fix everything that has gone wrong while Google Inc. has been cementing its position as the Internet’s most powerful company.

Mayer, 37, took over Tuesday as Yahoo’s fifth CEO in the past five years.

The surprise hiring announced late Monday indicates Yahoo still believes it can be an Internet innovator instead of merely an online way station where people pass through to read a news story or watch a video clip before moving on to more compelling Internet destinations.

“I just saw a huge opportunity to have a global impact on users and really help the company in terms of managing its portfolio, attracting great talent and really inspiring and delighting people,” Mayer said during a Monday interview with The Associated Press.

Both Google, the Internet’s search leader, and Facebook have been beating Yahoo Inc. in the battle for Web surfers’ attention and advertisers’ marketing budgets. Stock has been slumping since Yahoo Inc. balked at a chance to sell itself to Microsoft Corp. for $47.5 billion, or $33 per share, in May 2008.

Yahoo shares haven’t traded above $20 since September 2008.