Middlesex applied pressure during the early stages as Toby Roland-Jones opened up with a maiden and Ryan Higgins struck with his fourth delivery, searing back down the slope to trap Ben Charlesworth in front for a duck.
Opening partner Cameron Bancroft soon followed suit, lbw to a ball that Higgins moved the other way for 15.
Hammond added a valuable 41 in tandem with Ollie Price (17) before Tom Helm made the breakthrough, having the latter caught low at first slip to bring Bracey to the middle and Gloucestershire went to lunch on 101-3.
Hammond was first to 50 when he drilled Higgins to the cover fence and Bracey was not far behind.
Having swept Luke Hollman for successive fours to raise the century partnership, Hammond (78) looked on course for a ton of his own until he attempted a repeat of the stroke to de Caires and skied to mid-on.
With Graeme van Buuren given out caught behind two balls later without scoring and Bracey sweeping into the hands of deep midwicket for 56, Gloucestershire suddenly found themselves six down and under renewed pressure.
De Caires (3-45) continued to test the batters with flight and turn, but Price eased the tension by on-driving Roland-Jones to the boundary to take Gloucestershire beyond 200 and he and Zafar advanced steadily towards the finish line.
Zafar, who had top-scored with 86 in the first innings, applied the finishing touch as he cracked a de Caires full toss to the fence to finish unbeaten on 19, with Price alongside him on 34.
