After registering a five ball duck in his return to cricket in the first innings, Yorkshire captain Root, as well as opener Adam Lyth (54) found some excellent form as his side built a commanding lead of 268.
Root put on 98 for the third wicket with another talented young batsman, New Zealand's Kane Williamson, as the visitors made the most of the first good batting conditions of the match on the second afternoon.
Both were dismissed by Steven Finn (3/59) late in the day though, to keep Middlesex in the game. Finn will once again be pleased with his form as he returns to cricket.
The Tykes had earlier swept the hosts' batting line-up aside for just 123 thanks to a sustained display of accurate, aggressive fast bowling from Ryan Sidebottom (4/34), Jack Brooks (3/47) and Liam Plunkett (2/16).
Sidebottom was typically excellent in perfect conditions for his swing bowling, and was rewarded with the key wicket of Eoin Morgan, who top scored with 33.
Plunkett meanwhile bowled with genuine pace for a prolonged spell, clattering into the middle stump of both John Simpson and Tim Murtagh in a display which would have attracted the attention of the onlooking England selector Angus Fraser.