The loss in London sees Leicester drop down to eighth in the Barclays Women's Super League after a frustrating weekend in the capital saw them edged out by the narrowest of margins.
There were two changes from the Leicester side that beat Liverpool 2-0 last weekend to reach the semi-final of the Adobe Women's FA Cup, with Courtney Nevin and Emilia Pelgander making way for Lena Petermann and Yuka Momiki.
Despite creating the first opportunity with a free-kick into the Tottenham box, it was the hosts who took the lead through Vinberg who rounded off a quick counter-attack at the home of Leyton Orient.
City started applying the pressure but it was the hosts who continued to threaten and came close to a second when a long-range effort was well saved by Lize Kop, turning the ball onto the crossbar before CJ Bott finally cleared the danger.
The first shot on target for the Foxes came after half-an-hour when Momiki tried her luck with a curling effort from the edge of the box but Becky Spencer did well to get down to her right-hand side and make the stop.
The final piece of first half action came in injury time when Janice Cayman played a brilliant early cross into the path of Petermann who was a yard behind the ball as it went flashing past and out of play.
During the first 15 minutes of the second half, Leicester held a lot of possession but struggled to break Tottenham down, coming closest when Jutta Rantala struck the crossbar from a tight angle, after beating Ashleigh Neville on the left wing.
As the clock ticked by, Leicester became more frustrated at their position in the game, picking up yellow cards for fouls, but one positive change was the introduction of winger Deanne Rose who replaced Petermann, and looked dangerous in the final third.
City continued to probe until the end, and had a massive penalty shout at the death when there appeared to be contact from Neville on the Canadian forward, but defeat by Spurs sees the Foxes now focus on a home WSL clash to Brighton & Hove Albion next weekend.