FIFA International Soccer, 1994 (on most platforms), Electronic Arts. This is the first installment in the long series of FIFA-licensed games. It also seems to be the first to feature third-part brands on the field. Notice how the Adidas ad was replaced with a generic billboard on the Genesis version of the game. Compare all versions here.
Other games that came out in 1994 - NBA Showdown, NBA Live 95, PGA Tour Golf 3, NHL 95 had either no ads, house ads, or logos of the respective license holders.
FIFA Soccer 96, 1995, Electronic Arts. The game introduced a new level of realism into its class. The field adorned with billboards and looked especially realistic, although it is hard to tell whether there were any third-party ads (there is a billboard for "TADAL", but I don't know if it's a real brand). No third-party ads in other titles that year.
Cricket 97, 1996, Electronic Arts. More house ads in this and other games released that year (Melbourne House and Beam are development studios).
NHL 97, 1996, Electronic Arts (image source: Gamespot). The Windows version of the game featured ads for Coolair and possibly others.
NCAA Football 98, 1997, Electronic Arts. Second NCAA game (first one by Mindscape came out in 1994). Features an ad for Nokia.
NHL 98, 1997, Electronic Arts. Multiple third-party brands, most notably by Mastercard, Coca-Cola and Easton (manufacturer of sports gear - see site).
FIFA: Road to the World Cup 98, 1997, Electronic Arts. In Windows version, ads for Gillette, Mastercard. Versions for other platforms don't seem to have third-party ads.
X Games: Pro Boarder, 1998, Electronic Arts (image: Gamespot). Plenty of placeholders in this snowboarding game, and possibly third-party ads.
World Cup 98, 1998, Electronic Arts. Many third-party billboards, including ads by Opel, Mastercard, Snickers, McDonald's, Philips, Casio and JVC. The same ads are also present in the PS and N64 versions.
NHL 99, 1998, Electronic Arts (image: Gamespot). Cross-platform field ads for Wendy's, Bauer.
Apparently, no ads on NCAA Football 99, NBA Live 99, Knockout Kings boxing title, or Tiger Woods 99.