Before the explosive end to Hildreth's superbly-paced 94-ball innings, which contained seven fours as well as those three sixes from the first three balls of the 40th over, it seemed as if off spinner Ollie Rayner's fine eight-over spell of three for 31 had put Middlesex on top.
Somerset, looking to complete the double over Middlesex after beating them by six wickets at Taunton a fortnight ago, were given a fast start by Marcus Trescothick and Peter Trego, who put on 73 before Rayner struck his first blow in the ninth over of their innings.
Trescothick, having clubbed two sixes and four fours in 41 from 33 balls, was bowled middle stump as he played forward defensively to one that straightened in Rayner's opening over.
Trego was well held for a 28-ball 35 by keeper Adam Rossington, standing up to Harris's fast-medium on a docile surface, and Rayner then had the out-of-form England Test batsman Nick Compton brilliantly held one-handed for six by a leaping Neil Dexter at short mid-wicket.
Dexter claimed a more straightforward catch when South Africa all-rounder Dean Elgar chipped to short extra cover on 15, and only Hildreth stood firm as the Somerset slide continued as Alex Barrow (15) gave Paul Stirling a simple return catch and Arul Suppiah (10) hit Tim Murtagh to extra cover.
From 187 for six, however, Hildreth was joined by Craig Meschede, who drove Toby Roland-Jones into the pavilion for six, in a resourceful stand of 32 before Hildreth's own magnificent late assault on Harris boosted Somerset to a defendable score.