The commonly held belief that the 1990 Reds were the first team to do this is an urban myth. The 1984 Tigers went wire to wire, six years earlier.
http://www.retrosheet.org/boxesetc/04031984.htm
The Tigers and Indians were tied for first place at the end of play on April 3, which was opening day for both teams. The Yankees and the Orioles had both lost the day before, which put the five remaining teams in the division in a tie at zero wins and zero losses, half a game ahead of the Yankees and Orioles.
The Tigers and Indians both played night games in the Central Time Zone on April 3, so I can only assume they began at nearly the same time. The Tigers-Twins game lasted 2:10, while the Indians-Rangers game lasted 2:51, so even if the Indians-Rangers game started a half hour earlier than the Tigers-Twins, the Tigers-Twins game still would have ended earlier than the Indians-Rangers, putting the Tigers alone in first place, even if only for a few minutes.
The Tigers won their first nine games and 35 of the first 40. The Indians shared first place with the Tigers, until being beaten in their fourth game of the year in Kansas City. The Tigers did not relinquish first place at all that year.