Middlesex were left frustrated after centuries from Marcus Trescothick and Peter Trego rescued Somerset and set up the possibility of an intriguing final day at Taunton.
The hosts were 19 runs behind and four wickets down when Trescothick (124) and Trego (115 not out) came together to put on 181, dragging the hosts out of trouble.
Following his 4-67 in the first innings, Harry Podmore claimed three more victims to leave Somerset reeling, and James Harris (pictured) nipped Trescothick and Craig Overton out in the evening to give Middlesex hope again.
They will need to take quick wickets on Wednesday to set themselves an achievable target to chase.
In the morning, Middlesex established a first-innings lead of 145, adding 20 to their overnight score. James Fuller took his career-best innings to 93, while James Harris fell for 78.
Somerset collapsed to 59-3, trailing by 86, with Podmore bowling Johann Myburgh and having Chris Rogers caught, while Ollie Rayner picked up the wicket of James Hildreth.
Trescothick, though, remained untroubled, adding 67 alongside skipper Jim Allenby before the potentially match-saving stand with Trego.
In passing three figures shortly after tea, the veteran former England man became the second-highest century-maker in Somerset history.
When Harris snared both Trescothick and Craig Overton, Middlesex sensed an opportunity to once again turn the screw.
But Trego survived and together with Alex Barrow, added 33 more runs before stumps.
This post was last modified on 13/07/2016