Middlesex 141 for 1 (Robson 65*) trail Yorkshire 601 for 6 dec. (Hill 169*, Bairstow 160, Lyth 61, Bess 60*, Hollman 4-194) by 460 runs
Jonny Bairstow completed an excellent 160, and was usurped by George Hill's career-best 169 not out, on day two at Headingley as Yorkshire topped 600 in their first innings before Middlesex responded encouragingly.
Yorkshire have the advantage at the halfway stage of this Vitality County Championship promotion battle having posted 601 for six declared during the second half of the afternoon. But, given a benign pitch, Middlesex should be confident of claiming a draw having closed on 141 for one from 50 overs.
Bairstow, with a point to prove after being dropped from all England squads this summer, advanced from 107 overnight. The 34-year-old wicketkeeper-batter shared a record-breaking 238 for the sixth wicket with all-rounder Hill, who posted a first hundred of the season.
Leg-spinner Luke Hollman was Middlesex's standout bowler with four for 194 from 47 overs before Sam Robson, on the ground where he scored his only Test century for England - against Sri Lanka in 2014, led the way in their reply with a measured 65 not out.
The Bairstow-Hill partnership, which started during the early stages of the first evening, marks Yorkshire's highest sixth-wicket stand in first-class matches against Middlesex, and their innings total was joint ninth highest ever on this ground in first-class cricket.
It would be no great surprise to see second-placed Middlesex go close to matching that in a battle with a Yorkshire team who started this 11th fixture of 14 three points adrift in third place in Division Two.
This was not the rampaging Bairstow Yorkshire and England fans have come to expect in recent years. While he was still positive, he was extremely responsible.
That was in part due to the fact that when he united with Hill, Yorkshire were 242 for five and by no means certain of an imposing total. This is also not a pitch with oodles of pace. Timing the ball doesn't look to be entirely straightforwards.
And, of course, he has a point to prove to the England selectors.
Hill, who survived a missed-stumping on 64 before lunch off Hollman, has struggled with the bat this season. The ex-England Under 19 last scored a century in June of last year, for example, and this one came off 169 balls before lunch.
He was also calm and controlled, though did loft Hollman over long-on for six before lunch, where Yorkshire reached at 485 for six having started the day on 372 for five.
The hosts secured four batting bonus points, narrowly missing out on the maximum of five. But they did gain the second prize of limiting Middlesex to only one bowling point for taking five wickets inside the 110-over cut off.
With the gap between the two counties only three points coming into this game, that indicates that every point could be crucial in the promotion race.
Bairstow, who is not keeping wicket in this game, was bowled off an under-edge as he attempted to pull Hollman - the only Yorkshire wicket to fall on day two.
Hill and Dom Bess then shared an unbroken 121 for the seventh wicket, the latter contributing an unbeaten 60 in the sunshine.
Yorkshire's innings lasted 144 overs, and it was clear their first priority was not to lose the game, knowing a defeat would hand Middlesex a potentially defining result in the promotion race.
While Middlesex picked Hollman as their only frontline spinner, Yorkshire picked two in off-spinner Bess and left-armer Dan Moriarty.
After a short burst from new ball seamers Ben Coad and Jordan Thompson, they got to work and wheeled away through the majority of the evening.
Bess claimed the only wicket to fall when Mark Stoneman edged to slip for 27, leaving Middlesex 61 for one in the 19th over.
But Stoneman's opening partner Robson calmly saw his side through to close without further alarm, reaching his fifty off 105 balls.
He shared an unbroken second-wicket stand of 80 with Max Holden, who has 39 not out.
