Won by One
Defining Democracy, (Springer, 2012) has two appendices called Won by One and The People have Spoken. The first notes those occasions when parliaments or whatever have won or lost decisions or elections by a margin of only one vote or less than 1%... and sometimes, that one voter has been drunk, bribed, threatened or seduced. The second is a record of those referendums which have been won or lost by again less than 1%.
The data are not by any means complete, and we're constantly coming across other instances from countries near and far. Here are the latest Won by One and The People have Spoken lists, but if anyone knows of other instances, then do please contact this Institute.