After young defender Glen Johnson had equalised Adam Bolder's opener, a magnificent strike from Belgian striker Branko Strupar looked set to secure all three points for the visitors, until Soma ghosted in at the far post and blasted home from an acute angle with just four minutes remaining.
Sadly, the evening was soured by the dismissal of Richard Garcia - one of two red cards and five bookings handed out by referee Graham in a match that was never deserving of such a statistic.
The young Aussie, booked for a foul in the first minute of the second half, was harshly given his marching orders in the 73rd minute when he punched the ball into the ground in frustration at mis-controlling the ball and giving away a throw-in deep in the opposition half.
The man in black wasted no time in brandishing a second yellow to Garcia, and produced his second red card of the night in the final minutes when Derby full-back Francois Grenet was sent off for foul and abusive language.
There were also bookings for Grant McCann, Izzy Iriekpen and
17-year-old Anton Ferdinand - making an impressive full debut for
the second string after being called up as a late replacement for
Hayden Foxe - while Derby's Patrick Foletti probably became the
first goalkeeper ever to be booked for diving, despite being
allowed two minutes of treatment after apparently colliding with
Derby had enjoyed the livelier start and took a deserved lead in the 17th minute when the impressive Lee Morris raced down the left and pulled the ball back from the byline for Adam Bolder to slide into the net from 12 yards out.
However, Hammers' response was both determined and immediate. Just two minutes later, young defender Glenn Johnson rose to power home a header from a corner and bring the scores level.
The goal boosted confidence among the hosts and they began to settle down to some fluid and attacking passing, with the pace of striker Omer Riza causing problems in the Rams' rearguard.
Steve Bywater still had to be alert to keep out an effort from Ian Evett, but it was Hammers' who were presented with a glorious chance to take the lead on the stroke of half-time.
Riza skipped down the right to chase what looked a lost cause and got to the ball just as the Derby defender made his challenge - sending the young striker flying just inside the area.
With the help of his assistant, Graham pointed to the spot but Titi Camara stepped up and saw his kick palmed away by Foletti.
That proved a turning point as Derby came out for the second half with a renewed sense of optimism and began to take control.
Bywater was forced into a couple of simple saves before the visitors took the lead again in the 55th minute through Strupar, who curled a magnificent effort into the top corner from 25 yards out.
Once again, though, the Hammers fought back admirably and enjoyed the majority of possession for the remainder of the match, without much fortune in front of goal until captain for the night Soma popped up to smash home the equaliser.
Said boss Roger Cross afterwards: "Derby have a very good side and have won the Reserve league for the last two seasons.
"After the first 15 minutes I thought we were in trouble because they were causing us problems, but we came back well after their goal and evened things out.
"We missed a great chance to take the lead when Titi missed the penalty on the stroke of half-time but, after starting slowly in the second half, I thought we were the better side, showing great courage and deserved at least a point in the end.
"It was sad to see Richard Garcia sent off for something like that. I could understand if he had given away a free-kick and then kicked the ball away, but he simply punched the ball in frustration down in their corner and it bounced away a few yards.
"It was a competitive game but not a nasty one and it was disappointing to see the game end in that fashion.
"Overall, though, I was pleased with the performance from the lads and delighted for young Anton Ferdinand, who was called in late and was then up against probably the best player on the pitch in the first half, Lee Morris. Anton battled well, though, and didn't give up."
Team: Bywater, Ferdinand (Eastwood 83), Iriekpen, Johnson, Soma, Britton, Garcia, McCann, Courtois, Camara, Riza. Unused subs: Forde (GK), Khan, Lumsden, Ward.