Gale struck 13 fours and one six in the fifth first-class century of his career
Michael Vaughan made his highest first-class score for nearly a year before Yorkshire were rescued by Andrew Gale and Tim Bresnan against Worcestershire.
Resuming at 55-1 in reply to the hosts' 415 on day three at New Road, Yorkshire were reduced to 108-5 with Chris Whelan (4-98) removing Vaughan for 43.
Gale (101) and Bresnan (97) then shared 170 for the sixth-wicket to help the visitors save the follow-on.
Azeem Rafiq then plundered 62 not out to help the visitors close on 413-8.
Vaughan had shared a second-wicket partnership of 82 with Joe Sayers (44) before he was caught in the gully by Gareth Batty.
Ashley Noffke removed Sayers before Whelan sent Anthony McGrath and Jonathan Bairstow back to the pavilion to bring Gale and Bresnan together.
Gale struck 13 fours and a six in his 189-ball effort, with Bresnan weighing in with 11 boundaries of his own before he was caught by Daryl Mitchell off the bowling of Kabir Ali just short of his fourth first-class century.
When Whelan removed Ajmal Shahzad and Batty enticed Gale to hole out to mid-off, Rafiq and Matthew Hoggard combined to share an unbroken ninth-wicket stand of 79, with a draw now looking like the most likely result.
Worcestershire's Chris Whelan told BBC Hereford and Worcester:
"The sun came out this afternoon and the pitch flattened out a little bit.
"The boys have had a couple of long days in the field this week and I think everyone got a little bit tired.
"Maybe we let them off the hook a bit and we could have been a bit more cut-throat towards the end there."
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