It's consecutive away defeats for City who remain eighth in the Barclays Women's Super League with five points from their first seven games, after losing out to the Hammers in the capital.
There were three changes from the side that were beaten 1-0 by Brighton & Hove Albion last time out, as Amandine Miquel returned to a back four formation, introducing Yuka Momiki, Missy Goodwin and Hannah Cain, who made her first start since returning from injury, replacing Chantelle Swaby, Deanne Rose and the injured Sam Tierney.
Spurred on by the home support, West Ham saw more of the ball in the opening stages, first testing the gloves of Janina Leitzig through Riko Ueki before a glance to the touchline saw the linesman's flag raised.
Moments later, Cain was sent through on goal but at a tight angle, saw her low driven left-footed effort beat the Hammers' goalkeeper but drift the wrong side of the far post.
Struggling to find their mark on the game, the scores looked to be level heading into the break until Asseyi was played in behind and got to the ball before Leitzig, leaving an empty net for the French forward to score.
Fired up from their goal just before half-time, West Ham looked the more threatening as play resumed in Dagenham, and had shouts for a penalty claim, when Shana Chossenotte went for the ball in last-ditch tackle with Ueki.
Trying to force a way through the hosts' defence, Rose and Saori Takarada were introduced, in place of Janice Cayman and Cain, who was ramping up her involvement since coming back from injury.
In the final minutes, Leicester kept the pressure on but failed to break down a determined Irons' backline, who saw out their first win of the campaign, bringing them level on points with the Foxes, who head home for the first time in three weeks when they welcome Manchester United to King Power Stadium next Sunday for a 3pm GMT kick-off.