Martinez broke the deadlock early in the second half of the Barclays Women's Super League fixture but a late O'Brien goal from inches out resulted in the points being shared at Chigwell Construction Stadium.
Rick Passmoor made three changes to the side beaten by Arsenal last time out, with Janice Cayman, Jutta Rantala and O'Brien all coming out for Hlín Eiríksdóttir, Emily van Egmond and Noémie Mouchon.
An even first half
Mouchon started her first WSL game this season.
There was very little to separate the two sides during the first half, with the Foxes starting the strongest of the two, before the hosts came into the game more as it went on.
A quick start saw us with a free-kick on the edge of the Hammers' box, which Hannah Cain had two attempts at, but saw both her efforts blocked, before Sam Tierney worked an effort for herself, winning the ball back high up the pitch, but failed to find the target with her following shot.
Janina Leitzig was called into action on a couple of occasions as the hosts thereatened, but the scores remained goalless at the interval.
Martinez finds the net
City were beaten on Sunday afternoon in London.
Despite starting the afternoon bottom of the table, West Ham remained a dangerous outfit, with enough quality in the side to cause Leicester problems, and seven minutes from the restart they did just that.
A ball into the box received the faintest of touches from Martinez, but it was enough to unbalance both Sari Kees and Leitzig from close range, with both unable to clear the danger imposed.
A second goal of the season for the German centre-forward, West Ham looked good for all three points before some late mayhem in the capital.
O'Brien scores late on
The Foxes fought back to earn a point.
With the Foxes looking all but condemned to a fifth defeat of the season, a late free-kick into the box from Hannah Cain found Kees at the back post, who drilled the ball low and hard across goal, and it was substitute O'Brien who was on hand to take a touch and score from close range.
Preventing the Hammers from picking up their first win of the term, the result takes us up to ninth, sitting on six points, and remaining five above the Hammers.
We now look to Brighton & Hove Albion, who we take on next Sunday at 12pm GMT, with tickets still available online here - priced at £15 for adults, £10 for under-18s and £6 for under-10s.