The Register now owes the Times at least $2.464 million, the lawsuit said. The Times said its total damages may exceed $4 million.
They take the prize for an investigation that exposed tax fraud.
The award was one of many, including a total of 13 first-place honors, the Free Press garnered in the competition.
Coverage of natural disasters and health care as well as the making of a T-shirt took top honors Saturday night at the 2014 Online Journalism Awards, which ended the Online News Association Conference.
The Taos News owner is inducted into the New Mexico Press Association Hall of Fame.
The company walks away with 126 prizes.
The awards honor reporters from newspapers in two circulation divisions (over 50,000 circulation and under 50,000 circulation).
The investigative series, reported by four journalists, is having an impact on revamping state law.
He will investigate the causes, solutions and implications of homegrown terrorism.
Winners will be revealed at a September dinner in Chicago during the Online News Association's annual conference.
The organization will donate the $10,000 prize money to its own emergency relief fund.
The editorial writer and op-ed page columnist gets a $75,000 stipend.
More than 1,000 entries were submitted in 50 categories.