Steve Patterson struck with successive balls early in the afternoon session of day four but Middlesex pair Eoin Morgan and John Simpson then held firm at Scarborough.
Middlesex, chasing 422 to win this LV= County Championship, reached tea at 155-4 with 33 overs left in the day.
Patterson had Chris Rogers superbly caught one-handed by Adam Lyth diving to his left at second slip for 44 as the score slipped to 92-3 in the 37th over. He then trapped Paul Stirling lbw with the next ball.
Morgan resumed this evening on 23 and Simpson on 49.