The Lions levelled to take a share of the spoils in Tuesday night's Championship clash at Ashton Gate.
Davies, who signed from Derby in August, has been used as a second-half substitute in six games so far this season but made the most of his opportunity with a livewire display before departing injured after 70 minutes.
Darius Henderson made up for missing a golden chance to open the scoring early in the game when he headed in the equaliser seven minutes before half-time.
Aside from a good chance for Davies, neither side looked like scoring after the break and had to be content with a point that does nothing to add impetus to the stuttering starts to the npower Championship campaign for both teams.
The home side were full of purpose from the outset and after four minutes, Sam Baldock's cross was cleared only as far as Stephen Pearson on the edge of the area, but he dragged his left-foot shot inches wide.
At the other end, Liam Trotter cut open the City defence with a fine threaded pass but Henderson was unable to beat goalkeeper Tom Heaton with his low shot when well placed to score.
Davies then tried his luck from over 25 yards twice in quick succession - the first being parried away by Millwall keeper David Forde and the next going high over the crossbar.
There was a break in play midway through the half because of a puncture to the ball and soon after, Davies was trying his luck from distance once again as he sent a fierce shot narrowly over the crossbar.
The 24-year-old striker then made it fourth time lucky from distance on 28 minutes - although not with his foot but his head.
Cole Skuse's long ball over the top saw Forde scamper off his line out of his area and, under pressure from Baldock, headed the ball only as far as Davies, who in turn guided a header with perfect precision into the net from 30 yards.
But the visitors responded 10 minutes later when Henderson bagged his seventh career goal against Bristol City when heading home James Henry's cross from the right.
Chris Wood almost gave Millwall the lead before the break, but he could not get enough power on his header from Shane Lowry's cross as Heaton easily claimed.
Derek McInnes' men had the first chance of the second half when Davies nodded down a Neil Kilkenny cross into the path of Albert Adomah but, off balance, he struck over the bar from close range.
Davies then curled a free-kick wide, before the busy frontman hit the side-netting with a shot from Skuse's delivery - following a quick counter-attack from the hosts.
As the rain fell, the game became increasingly more scrappy as the half continued - with neither side able to find the killer ball in the final third.
Substitute Andy Keogh glanced a header wide for Millwall with three minutes to go, while Henderson dragged a shot wide in injury time as the visitors ended the game the better.
