This started a winning streak for them of 11 games, which brought them into second place, seven games behind the Chicago Cubs in the standings. During that stretch, McGraw was able to earn two saves, bringing his total for the season to 12. As a reliever, he had a record of 8–2 with an earned run average of 1.47.

When the Chicago Cubs came to New York on September 8 to start the first game of a pivotal two-game series against the Mets, they had spent the previous 156 days of the season in first place in the National League East, and it appeared as though they would win the division. Both games were won by the Mets, bringing them to within a half game of the Cubs in the standings. The next day, the Mets defeated the Montreal Expos in both games of a doubleheader to take the series. During the 1969 season, the Mets made history by moving into first place for the very first time thanks to a loss suffered by the Cubs, who had finished the season with a record of 9–17 in their final 26 games.

On September 15, Steve Carlton of the St. Louis Cardinals set a record by striking out 19 Mets batters while pitching in a game that the Mets ultimately won 4–3 against the Cardinals at Busch Stadium thanks to two home runs by Ron Swoboda that scored two runs each. The victory in this game went to McGraw, who pitched the final three innings without allowing any runs to be scored against him. The New York Mets defeated Carlton and the Cardinals by a score of 6–0 on September 24, thereby clinching first place in the National League East. Donn Clendenon contributed to the victory by hitting two home runs for the Mets in the game. The Mets finished the season with 100 wins against 62 losses, an eight-game lead over the Cubs in second place. Their final record was 39 wins out of their final 50 games played.

The second game of the 1969 National League Championship Series was McGraw's first experience in the postseason, and it was the only postseason game he played in 1969. Koosman was lit up for six runs by the Atlanta Braves in the first inning, but Ron Taylor and McGraw held the Braves scoreless in the remaining innings to secure an 11–6 victory for the Mets. In the 1969 World Series, which was played against the Baltimore Orioles, he did not make an appearance.

Ya gotta believe!

In the early 1970s, McGraw established himself as one of the best closers in the National League, and he had a breakout year for his career in 1972. At the All-Star break, he had a record of 3–3 with an earned run average of 2.01 and fifteen saves, which earned him a spot in the All-Star game for the first time. In order to earn the win in the National League's come-from-behind victory of 4–3, McGraw pitched two innings, allowing only one hit while striking out four batters. During the course of the season, McGraw compiled an 8–6 record with a 1.70 earned run average, allowed just 71 hits while pitching 106 innings, and established a Mets record with 27 saves that stood until 1984.

Despite the fact that McGraw had a less successful year statistically in 1973, he may have been the most valuable player on the team because of the leadership role he assumed for the team that won the league championship. The Mets had dropped to the cellar of the National League East, and they had remained there through the 30th of August. On August 31, McGraw was the winning pitcher for the Mets as they beat the St. Louis Cardinals in extra innings. This victory allowed the Mets to move out of last place and into second place in the National League. The victory raised McGraw's record to 2–6 despite his 5.05 earned run average (ERA).

The rest of the season, McGraw had a record of 3–0 with an earned run average of 0.57 and ten saves. The Mets, on the other hand, went 20-8 from that point forward to pull off the unbelievable feat of winning their division. It was on July 9 during a team meeting that McGraw yelled out the words "Ya Gotta Believe," which went on to become a popular rallying cry for the Mets. Mets Board Chairman M. Donald Grant was trying to encourage the team at the time. The article "New York Mets: A Rallying Cry is Born" can be found at the following URL: http://www.bigleaguesmag.com/new-york-mets-a-rallying-cry-is-born/. The March 21, 2013 issue of Big Leagues Magazine Retrieved 2013-06-11. It's possible that he was the only person who believed the Mets could actually win the World Series when he uttered the famous phrase. But eventually, after hearing McGraw say it time and time again and witnessing him work his magic in the ninth inning, the Mets came to believe it themselves. They defeated the Pittsburgh Pirates by a score of 10–2 on September 21, which propelled them into first place, and they clinched the division title on the last day of the regular season. Between the years 1970 and 1980, this was the only season in which neither the Philadelphia Phillies nor the Pittsburgh Pirates were crowned champions of the National League East.

McGraw carried over his dominant pitching performance into the postseason, where he faced the Cincinnati Reds in the 1973 National League Championship Series and appeared in five of the seven games of the 1973 World Series against the Oakland Athletics. During the National League Championship Series, McGraw pitched five innings over the course of two games and did not allow a run. Even though he was unable to secure the save in game two of the World Series, he went on to win the game by pitching three scoreless innings in extra innings.

The Philadelphia Phillies received McGraw, Don Hahn, and Dave Schneck from the New York Mets in exchange for pitcher Mac Scarce, outfielder Del Unser, and catcher John Stearns, whom the Philadelphia Phillies had drafted second overall in the 1973 Major League Baseball Draft. The trade took place on December 3, 1974. Due to the fact that McGraw had experienced shoulder problems throughout the 1974 season, it appeared as though the Mets were trying to get rid of damaged goods when they made the trade. After the deal, he received a diagnosis of a simple cyst, and he was able to make a full recovery after undergoing successful surgery to remove it. After his career with the Mets, McGraw retired as the franchise's all-time leader in saves, games pitched, and games finished.

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