Middlesex 334 (Eskinazi 178*) and 36 for 2 require a further 198 runs to beat Warwickshire 334 (Clarke 83, Lamb 51) and 233 (Trott 99, Helm 5-59) by 32 runs
A compelling denouement is in prospect at Edgbaston where Middlesex will resume on the final morning of their crucial Specsavers County Championship tussle with Warwickshire on 36 for 2, needing 234 to win.
After both teams totalled 334 in their first innings, the third day saw Jonathan Trott, captaining Warwickshire with Ian Bell sidelined by a sore elbow, prop up his side's second innings with 99.
Trott defied skilfully on a pitch offering some variable bounce and against a Middlesex attack which performed admirably to compensate for the absence of Steve Finn and Toby Roland-Jones. Tom Helm led the way with his maiden five-for, bowling with pace and aggression to take the first two wickets and the last three to end with 5 for 59.
Victory here would be a huge boost to either side in their survival battle, and the match is intriguingly poised going into the final day with all results still possible.
After Middlesex resumed on 302 for 6, they added only another 32. Steve Eskinazi's career-best 179 was ended by Keith Barker's first ball of the morning which knocked out off-stump.
Ollie Rayner played on to Barker before Rikki Clarke had Helm caught by Andy Umeed at first slip and Tim Murtagh caught behind.
Warwickshire's second innings was quickly damaged by Helm whose excellent new-ball spell accounted for William Porterfield, caught at second slip, and Andy Umeed, lbw.
After Trott and Sam Hain added 63, Middlesex struck twice again when Hain edged Ryan Higgins to second slip and Matt Lamb nicked James Harris behind.
That was 85 for 4 but Trott and Ambrose (44, 61 balls, three fours) knuckled down to add 94 in 23.3 overs before Ambrose fell lbw to Dawid Malan in the last over before tea.
Murtagh removed Clarke with a ball which exploded off a length and looped off the bat to gully. Barker clipped Malan to midwicket and then Helm returned to wrap up the tail with three wickets - Trott, who pulled a short ball straight to Nick Compton at midwicket, Jeetan Patel and George Panayi - in eight balls.
In 13 overs before the close, Middlesex lurched to 1 for 2 after Sam Robson fell lbw to Clarke, completing a pair, and Eskinazi edged Barker to Ambrose, but Malan and Compton saw it calmly through to the close.