Elie won two NBA championships with the Rockets, one in 1994 and one in 1995. During this period, Elie was dubbed the "Junkyard Dog" by his teammates. One highlight of Elie's career came when he hit a game-winning three-pointer in Game 7 of the 1995 Western Conference Semifinals against the Phoenix Suns to break a tie with 7.1 seconds. The shot is called the "Kiss of Death" by Rockets fans, as Elie made a taunting kissing gesture towards the Suns' bench after the shot. While Elie was a key role player for the Rockets off the bench throughout the regular season and the playoffs, he became a starter in the 1995 NBA Finals. This move paid off for the Rockets, as Elie averaged 16.3 points per game in the Finals while shooting 65% from the field.