As Paul noted in a post below, and as Jason Kottke has documented in some detail, the opening of the New York Times archive has been a boon to the armchair historian. So inspired, I searched for the first appearance of Babe Ruth in the Paper of Record. That mention came on April 14, 1914, about halfway into the recap of a pre-season matchup in Baltimore between the New York Giants and the homestanding Orioles, then of the International League. Here's the fourth paragraph of the piece:
"Babe" Ruth, a youngster, opposed the Giants, who made nine hits off him. Four double plays, all started by Claude Derrick, who handled twelve outs of the thirteen chances, kept the Giants from scoring more runs.
By now most fans know that Ruth began his career as a pitcher, and here we see him losing a 3-2 decision, but giving a hint at the talent that would make him one of the game's top hurlers in the coming years. Yes, he allowed nine hits (he also walked a pair and hit two batters). But in addition to the four double-plays mentioned above, he struck out 7 in a complete game effort against a Major League club, and he was just 19 at the time. In retrospect, it's amusing to note that he hit in the pitcher's traditional ninth position, and went 0-for-4. Ruth was sold to the Red Sox a few months later, in July. It's also worth noting how much the game has changed over the years. Fielding, in the Deadball Era, was much more of a focus, as the emphasis on shortstop Derrick's play indicates.
A few more interesting facts from the story. Though Orioles manager Jack Dunn promoted the game by promising that Giants manager John McGraw would start one of his two star pitchers—Christy Mathewson or Rube Marquard—attendance was poor: about one thousand fans, and many of them were overflow from the rival Federal League contest between the Baltimore Terrapins and the Buffalo Federals, scheduled concurrently. That game drew twenty-five thousand. The Terrapin team, curiously, was run by Ned Hanlon, McGraw's mentor, and also a participant in Spalding's World Tour. In fact, there was never much chance of McGraw starting one of his two big guns; the National League schedule began in two days, and he wanted them rested. Instead, he gave the ball to Ferdie Schupp, who was later relieved by Bunny Hearn. Finally, Fred Merkle, famous for his pennant-costing boner in 1908, made an error in this game.