The Japan international struck in both halves as Peter Bosz guided Vitesse to within five points of league leaders Ajax.
Havenaar's opening goal came in the 14th minute and, after Marko Vejinovic had doubled their lead, the 26-year-old found the back of the net again to seal the win.
Roda's chances were dealt a blow just before Vejinovic's strike with the dismissal of Roly Bonevacia for a professional foul on Havenaar.
The striker should have had his hat-trick late on, but his close-range header was deflected wide by the challenge of a Roda defender.
Defeat leaves Roda bottom of the table, six points from safety after ADO Den Haag collected a point against NAC Breda
After a mix-up in the NAC defence, Roland Alberg earned Den Haag a point with his third goal of the season, a point that moves them onto 28 points and extends their unbeaten run to four games.
Bryan Ruiz kept PSV's winning run intact with a 90th-minute strike to earn a 3-2 victory over Go Ahead Eagles.
PSV found themselves 2-0 down at half-time following goals from Jarchinio Antonia and Erik Falkenburg, but a spirited comeback saw Phillip Cocu's men make it five league wins in a row.
Memphis Depay and Jurgen Locadia dragged PSV level before Ruiz struck the killer blow late on.
Meanwhile, Zwolle and NEC shared six goals in a thrilling 3-3 draw.
Zwolle, pushing for a top-eight finish, found themselves two goals ahead after 35 minutes only for Soren Rieks and Michael Higdon to bring NEC level a minute into the second half.
Joost Broerse put the hosts again just before the hour, but Rieks netted his second of the game to earn NEC a share of the points.
