Wilson had declared victory more than a week ago, but Madrid waited until after Monday's Bernalillo County canvass to concede.
The canvass gave Wilson a 875-vote lead. Bernalillo's canvass -- the state's largest -- gave Madrid the edge, with 95,320 votes to Wilson's 94,086.
But Wilson overcame that margin by defeating Madrid in three of the four other counties that comprise the 1st District.
The overall tally showed 105,921 votes for Wilson and 105,046 for Madrid.