After conceding two goals in the dying moments against Aston Villa last week, Tony Carr's team was left stunned again as City struck a last minute equaliser to deny them three points.
After midfielder Graeme Carrick had been forced off with a hamstring injury in the seventh minute, Hammers were dealt another blow eighth minutes later when the visitors took the lead with a well-worked goal.
However, we bounced back on the half hour mark, when Freddy Eastwood chased a lost cause on the left and managed to cut the ball back for Billy Mehmet, who finished well from close range.
That gave the hosts renewed confidence and, on the stroke of half-time, the tide was turned when Phil Lumsden broke forward from midfield to receive a through pass and coolly clipped the ball over the City goalkeeper to put his side 2-1 up.
That should have provided a platform for Hammers to go on and build an unassailable lead in the second half, but the wet and windy conditions played a part as they struggled to build any passing rhythm against their hard-working and determined opponents.
Despite failing to add to their tally, though, Hammers appeared to be heading for victory as keeper Glenn Jackson remained relatively untroubled.
That was until the 89th minute, when he parried out a fierce shot from the edge of the penalty area, only for a City forward to follow up and net the rebound and claim a share of the points for his side.
Said Tony Carr afterwards: "It's obviously disappointing to have conceded a last minute equaliser for two weeks running but, if I am honest, we didn't really do enough to deserve the win today.
"Bristol City were a decent side who were physically a lot stronger than us and, although I couldn't see them scoring as the game wore on, the threat was always there.
"We had a bad start, losing Graeme Carrick early on with an injury that now leaves him doubtful for our FA Youth Cup tie in 10 days time, and then conceding the first goal.
"The players responded well, though, and when we scored right on half-time, I felt confident we would go on to win the game comfortably.
"It just didn't happen in the second half, though. The pitch was in poor condition because of all the rain and we failed to find any fluency. Neither side deserved to win the game, so I would say the draw was a fair result overall."
Team: Jackson, McClenahan, Tattam, Laws, Blewitt, Lumsden, Akinsete (Pearson 85), Carrick (McMahon 7), Eastwood (Wright 85), Mehmet, Cole. Subs unused: Sealey.
Meanwhile, goals from San Lee and Mark Noble weren't enough for the under-17s in their home clash against the Robins, as they lost 3-2 - also for the second week running following last week's defeat at Southampton.
The Hammers enjoyed a fantastic start, as they opened the scoring after just five minutes when Ollie Allen cut the ball back for Korean striker San Lee to slot home, and Kevin Keen's side virtually dominated for the remainder of the first half.
They doubled their advantage 15 minutes into the second half, when Noble raced on to a through ball from Danny Bunce and finished well to secure the two goal cushion that should have made sure of the three points.
However, after missing three or four excellent opportunities to score the third clinching goal, Hammers also made mistakes at the other end, allowing the visitors to score in the 65th, 75th and 85th minutes to snatch an unlikely victory.
The misery was compounded in the final minute when goalscorer Noble was sent off after receiving two yellow cards in the space of a few seconds for persistent dissent towards the referee.
"It really was a game we should have won," said Kevin Keen afterwards, "and we only have ourselves to blame for the fact that we didn't."
"After going 2-0 up, we wasted several good chances to make the game completely safe, and all three of their goals came from defensive mistakes by us.
"It's very unfortunate, and things just don't seem to be going for us at the moment, but it is a good test of character for these young players and we will work hard to get back to winning ways."
Team: Behcet, Henry (White 85), Parrington, Ketchell, Bunce, Yao, Noble, Tucker, Cohen (Welsh 60), Lee (Ephrain 70), O Allen. Subs unused: Shaw, Singh.