The team said before the game against the Baltimore Orioles that it was not expected to be a sellout at Fenway Park.
The streak began in May 2003 and includes the postseason. The string broke the record of 814 set by the NBA's Portland Trail Blazers from 1977-95.
Boston's streak of 794 regular-season sellouts also is the longest in major pro sports history. The previous longest regular-season streak in major league baseball history was 455 set by the Cleveland Indians from 1995-2001.
"The streak is a reflection of a phenomenal period of baseball in Boston and of America's greatest ballpark," Red Sox owner John W. Henry said in a statement. "But more than that, it is a testament to the baseball passion of New England fans. As we close the book on this incredible era, we look forward to another with a renewed certainty that the next couple of generations of Red Sox fans will also be enjoying baseball at the ever magical Fenway Park."
The sellout streak began on May 15, 2003, when the Red Sox beat the Texas Rangers 12-3 as Pedro Martinez pitched six scoreless innings before 32,485 fans. Seating capacity was expanded after that and the streak continued through Monday's home opener, a 3-1 win over the Orioles with an official attendance of 37,008.
The average attendance during the streak was 36,605, the Red Sox said.
In recent seasons, there were hundreds, sometimes thousands, of empty seats at Fenway Park, which opened in 1912. The Red Sox said last season that attendance is based on tickets distributed, such as those given to charities, and not on the actual number of fans who attend games.
The Red Sox won the World Series in 2004, the second season of the streak, and again in 2007. But they missed the playoffs the past two years and finished at 69-93 last season in Bobby Valentine's only season as their manager.
During last season, they traded pitcher Josh Beckett, first baseman Adrian Gonzalez and left fielder Carl Crawford, who were due $261 million from 2013-18, to the Los Angeles Dodgers.
In the offseason, the Red Sox hired John Farrell as manager and overhauled their roster, avoiding star free agents and long-term deals.
"We are proud of this historic achievement," Red Sox president Larry Lucchino said of the streak. "Over the past ten years, more than 30 million, many among the most sophisticated baseball fans in America, have purchased tickets to see games at Fenway Park. Never in that period was there a crowd less than 32,000. No other club in Major League Baseball can make that statement."