In Rudy Tomjanovich's second full season as head coach, the Rockets began the 1993-94 season by tying an NBA record with start of 15-0. Led by Hakeem Olajuwon, who was named the MVP and Defensive Player of the Year, the Rockets won a franchise-record 58 games. The Rockets in the second round of the playoffs recovered from losing the first two games at home to the Phoenix Suns in the second round of the playoffs after blowing multiple big leads in the first two games, eventually winning in seven games to advance to the NBA Finals. This series is widely regarded as the birth of the term nickname "Clutch City". Houston once again went down by three games to two to the New York Knicks, but managed to win the last two games on their home court, and claim their first championship in franchise history, of which at the end of Game 6 Olajuwon blocked a championship-winning 3-point field goal attempt by John Starks, forcing a Game 7. Olajuwon was awarded the Finals MVP, after averaging 27 points, nine rebounds and four blocked shots per game.
1994–1995 season
The Rockets initially struggled in the first half of the 1994-95 season, and ended up winning only 47 games, which was 11 games lower than their previous year's total. In a midseason trade with Portland, the Rockets obtained guard Clyde Drexler, a former teammate of Olajuwon at the University of Houston, in exchange for Otis Thorpe. Houston entered the playoffs as the sixth seed in the Western Conference, but managed to defeat the 60-22 Utah Jazz in the first round, winning the last two games after being down 2-1 including the decisive Game 5 road win. They fell behind 3-1 to the 59-23 Phoenix Suns in the second round, but won three straight to win the series, and became only the first team in NBA history to overcome both a 2-0 and a 3-1 series deficit in a seven-game series during the same postseason. The Rockets then beat the 62-20 San Antonio Spurs in the conference finals, to reach the Finals against the Orlando Magic, led by Shaquille O'Neal and Anfernee "Penny" Hardaway. When Houston swept the series in four straight games, they became the first team in NBA history to win the championship as a sixth seed, and the first to beat four 50-win teams in a single postseason en route to the championship. Olajuwon, who had averaged 35.3 points and 12.5 rebounds against the Spurs and regular-season MVP David Robinson in the conference finals, was named the Finals MVP, becoming only the second player after Michael Jordan to win the award two years in a row. Shaquille O'Neal, Kobe Bryant, and LeBron James have since accomplished this.