oh-my-zsh history completion

I have found the solution to my problem in the ZSH documentation. Oh-my-zsh seems to map the ↑ and ↓ Keys to something like

bindkey '\e[A' history-search-backward
bindkey '\e[B' history-search-forward

Which yields the exact behavior I described above. The ZSH Documentation describes the behavior of history-search-backward as

Search backward in the history for a line beginning with the first word in the buffer.

What I wanted instead was the following mapping, which I inserted into my ~/.zshrc:

bindkey '\e[A' history-beginning-search-backward
bindkey '\e[B' history-beginning-search-forward

The behavior of history-beginning-search-backward is as follows:

Search forward in the history for a line beginning with the current line up to the cursor. This leaves the cursor in its original position.

Also, if \e[A doesn't work for the up or down arrows, press <ctrl-v><KEY (e.g., up arrow)> in another terminal which gives ^[OA. Then you can use this instead of \e[A. The process is described here: http://zshwiki.org/home/zle/bindkeys

I wanted the same behaviour for zsh with oh-my-zsh installed and found plugin history-substring-search.

I achieved the same behaviour described above by adding the plugin to my ~/.zshrc:

plugins=(git brew npm history-substring-search)

I guess this plugin did not exist back when this question was raised. Just an alternate way to achieve the same thing.