Yorkshire captain Andrew Gale took his aggregate to 375 in two Championship innings as his side ran up a total of 390 and then reduced Middlesex to 16-1 before bad light and rain ended play just after tea at Lord's.
Gale, who batted almost nine hours for his 272 against Nottinghamshire at Scarborough last week, had been at the crease for another five hours scoring 103 when he was leg-before to off spinner Ollie Rayner.
Gale had lost Alex Lees - with whom he had shared a third-wicket partnership of 145 to take Yorkshire to 215-2 - to the first ball of the morning from James Harris, who had recovered from the side strain which had forced him out of the attack after only 4.3 overs the day before.
Lees nibbled at it and was caught behind for 100, his first championship century in only his third match, after facing 223 balls and hitting 11 fours.
Next over, Joe Sayers, sadly out of form and only back in the side because Gary Ballance is suffering from a virus, was leg-before to Tim Murtagh for one but Gale found another willing partner in Adil Rashid, the leg-spinner who is emerging as a prolific middle-order batsman.
Rashid, whose average this season was trimmed to a modest 169 when he was out for a duck against Nottinghamshire, should have gone again without scoring when he edged his eighth ball from Murtagh to first slip but Joe Denly put down a straightforward catch.
He made Middlesex pay with some glorious straight drives and by the time Gale, who had never looked like getting out, surprised everybody by falling leg-before as he tried to whip Rayner through the onside, they had put on 109 for the fifth wicket.
Yorkshire's target then was a fourth batting point but with seven needed off the 110th over, Rashid was leg-before playing across the line to Harris after making 72 off 109 balls with 12 fours.
They had to settle for a few more runs from the tail and a total which was looking imposing when Middlesex's reply got off to a terrible start, as Steven Patterson found bounce and movement to have Sam Robson caught at second slip for just five.
The weather closed in after 5.2 overs of the Middlesex innings to bring an early end to proceeding.