Ovechkin scored three times against the Ottawa Senators on Thursday and had four goals against the Montreal Canadiens on Saturday.
The record for goals by one player through the first three games of the season is nine, by Reg Noble of the Toronto Arenas and Joe Malone of the Montreal Canadiens in 1917-18, the first season of the NHL.
Ovechkin has one hat trick against the Lightning, a four-goal game Dec. 10, 2013. He has scored two goals in a game against the Lightning on eight other occasions.
The Lightning have allowed eight goals on 84 shots in its first two games.
Lightning center Steven Stamkos has four assists but no goals in his first two games.