Middlesex need just 44 runs with eight wickets in hand to claim a win over Durham that would see them leapfrog their opponents into third place in the LV= County Championship Division One standings.
Graham Onions produced another inspired showing for Durham but his 7-62 in Middlesex's first innings appears unlikely to deny the home side as they closed the second day on 103 for two at Lord's.
After the fall of 15 wickets on the first day, 17 went down on the second as bowling greatly outshone batting on a blameless pitch before Adam Voges and Eoin Morgan shared an unbroken stand of 62 in 15 overs to put Middlesex within sight of victory.
Onions took all five of Middlesex's remaining wickets to help dismiss the hosts for 168 and leave them with a first-innings lead of 25.
While looking at his most dangerous when shaping the ball away from the right-handers, Onions snared his first two victims via leg-side catches for wicketkeeper Phil Mustard.
Neil Dexter was first to go for 48, gloving an intended hook, and Ollie Rayner somehow paddled the next ball just out of long leg's reach for six. They were the only runs he scored before he too fell to Onions.
Regulation edges accounted for the rest of Onions' victims, with two more catches for Mustard and one for Michael Richardson at third slip.
The clatter continued as Durham started their second innings with opener Mark Stoneman, out to Tim Murtagh's second ball in the first innings, falling lbw to the fourth this time.
Keaton Jennings was then powerless to deal with a fine ball from Finn, which flew off the edge to Sam Robson at third slip.
After Will Smith and Ben Stokes applied themselves diligently in a fourth-wicket stand of 65, both fell carelessly.
Smith went for 30 when he lobbed an intended pull off Murtagh to mid-on and, after making the game's only half-century off 92 balls, Stokes went down the pitch to off-spinner Rayner's fourth ball and was stumped.
Paul Collingwood was bowled off his pads first ball by Corey Collymore and when the last three wickets went down for four runs Durham were all out for 171.
Middlesex had 26 overs to bat and quickly lost Robson, Division One's leading scorer. He went into the match needing 13 for 1,000 championship runs and remains six short and after edging Chris Rushworth to third slip.
Joe Denly raced to 32 off 33 balls before being surprised by extra bounce from Onions and lobbed a catch to cover as the Durham ace claimed another victim.
That made it 41 for two and Durham thought they had a vocal caught behind appeal rejected with England man Morgan on nought. Voges also survived a couple of scary moments before both settled down to prove the pitch held no terrors and close on 24 and 36 respectively.