WASHINGTON, Nov 17 (Reuters) - Alaska Republican Senator Lisa Murkowski on Wednesday became the first U.S. senator in half a century to win as a write-in candidate.

Election returns from a lengthy counting process in Alaska showed that Murkowski narrowly defeated conservative Tea Party movement favorite Joe Miller to win re-election.

Miller, backed by former Alaska Governor Sarah Palin, had defeated Murkowski in the Republican primary campaign in Alaska, prompting Murkowski to mount a write-in campaign.