Suzuki singled off Toronto starter RA Dickey in the first inning to reach the landmark, prompting a lengthy break in the game as his Yankee team-mates came out of the dugout to congratulate the Japanese outfielder, who then removed his cap to bow to the crowd.
Suzuki now has 2,722 hits in Major League Baseball, the rest having coming in his native Japan before he signed for the Seattle Mariners in 2001.
He becomes only the third player in the history of professional baseball to reach 4,000 hits following Pete Rose and Ty Cobb.
After the moment of history had been made, the Yankees needed a two-run homer from Alfonso Soriano in the eighth inning to secure the win.
It was a fourth win in a row for the Yankees as they bid to make a late run at the post-season.
They are 6.5 games back on the AL East-leading Boston Red Sox, who routed the San Francisco Giants 12-1 as Stephen Drew and Will Middlebrooks went deep.
That saw the Red Sox move one game clear of the Tampa Bay Rays, who lost 4-2 to the Baltimore Orioles as Adam Jones and Chris Davis hit home runs.
The Texas Rangers completed a sweep of the Houston Astros as Elvis Andrus' sacrifice fly in the bottom of the ninth lifed them to a 5-4 success.
The win sees Texas move 2.5 games clear in the AL West as the Oakland Athletics lost for a second successive day, 5-3 to the Seattle Mariners as Brendan Ryan collected three RBIs.
Late runs powered the Detroit Tigers to a 7-1 win over the Minnesota Twins in a game scoreless through the first six innings, while a grand slam from Dayan Viciedo lifted the Chicago White Sox in a 5-2 victory over Kansas City.
Nick Swisher's two-run homer helped the Cleveland Indians beat the Los Angeles Angels 3-1.
In the National League, Carlos Beltran and Allen Craig homered for the St Louis Cardinals in an 8-6 win over the Milwaukee Brewers that put them within one game of the Pittsburgh Pirates - 2-1 losers against the San Diego Padres - in the NL Central.
Jason Heyward suffered a fractured jaw when struck in the face by a pitch but his Atlanta Braves team-mates won without him, beating the New York Mets 4-1 to remain 15 games clear in the NL East, while the NL West-leading Los Angeles Dodgers moved 8.5 games clear with a 4-1 win over the Miami Marlins.
The Cincinnati Reds led 8-0 early on but were left hanging on to beat the Arizona Diamondbacks 10-7 while the Washington Nationals blew one five-run lead before building another in an 11-6 victory over the Chicago Cubs.
Michael Young drove in Carlos Ruiz to give the Philadelphia Phillies a 4-3 walk-off win over the Colorado Rockies.