Finn bowled with pace and confidence in collecting figures of 4/30 - including his returning England teammate Joe Root for a duck - as Middlesex dismissed Yorkshire for just 178 in the first innings.
He was more than ably assisted by opening bowlers James Harris (3/42) and Tim Murtagh (3/48), as the trio combined expertly to reward captain Chris Rogers for inserting Yorkshire after winning the toss.
They were frustrated by a fine unbeaten 56 from Liam Plunkett though, who gave the score some respectability after coming in at a precarious 98/6. Plunkett's counter-attacking knock took just 55 balls and included ten boundaries.
Middlesex were soon on the back foot in their response, losing their two openers and lynchpins Chris Rogers and England hopeful Sam Robson with the score at only 20. In form seamer Jack Brooks claimed both scalps.
Dawid Malan and Eoin Morgan rallied well, taking the score past 50, but with bad light looming Ryan Sidebottim removed Malan for a fluent 31 to ensure Yorkshire ended the day on a high.