Ex-England left-arm seamer Ryan Sidebottom took three wickets in the first over of the game and finished with figures of 5-18, to surpass 700 first-class wickets.
"That first over epitomised what Ryan is all about and to get his 700th wicket as well, he's been a fantastic bowler over the years and there's still a lot of life left in him," Yorkshire cricket director Martyn Moxon told the BBC.
Gillespie, 40, was appointed Yorkshire coach in 2011 and was a candidate to lead the England team this year before the job was given to fellow-Australian Trevor Bayliss.
Yorkshire, who have England batsmen Joe Root, Adam Lyth, Jonny Bairstow and Gary Ballance in their squad, have won the championship a record 32 times with one shared title.
They arrived at the home of cricket for the third-last match of the season 43 points ahead of Middlesex whose failure to secure any batting bonus points ended their hopes of finishing top.
"The first win is really special, but given the circumstances this is probably a bigger achievement than winning last year," Moxon said.
"To combine developing England players with domestic success is a fantastic effort from everyone involved."
(Reporting by Ed Osmond, editing by Pritha Sarkar and Toby Davis)
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