Anderson had five 3s — all in the first half — and grabbed 11 rebounds to lead the Magic. Howard posted his 20th double-double of the season.
Orlando fell two shy of its season high for 3s and set a team record with 42 attempts.
The Magic have won four of five since their season-high four-game losing streak. They have also beaten Miami in nine of their last 11 meetings in Orlando.
Dwyane Wade led the Heat with 33 points, but had only 11 after halftime. LeBron James added 17.
The Heat had their three-game winning streak snapped. Miami continues its six-game road trip Friday at Washington.
In the middle of a stretch of 20 games in 32 days before the All-Star break, the Magic got a rare day off from game action Tuesday. They seemed energized from the opening tip against the Heat, racing out to a 17-point lead in the first half.
That cushion was 16 at the start of the fourth quarter thanks to all those 3s.
The Heat got within 89-80 on a basket by Chris Bosh before Jameer Nelson's 3 from the corner pushed the Magic's advantage back to 12 with 3:53 to play. The Heat never got any closer.
Orlando was shooting better from the 3-point line than from the field at one point in the fourth quarter. The Magic finished the night at 42 percent from the floor (35 for 83) and 40 percent (17 for 42) from 3-point range.
Miami shot 47 percent from the field (36 for 76) but had only five 3-pointers.
The Heat also held a 40-30 advantage on points in the paint, but Orlando led 23-9 in second-chance points.
Anderson's 3-pointer gave the Magic their biggest lead of the first half at 44-27.
The Heat responded by closing the half with a 24-9 spurt — including the final 12 points by Wade — to go into halftime trailing by only three.
Wade finished the half with 22 points, while Anderson's five 3s and 24 points paced the Magic.
Howard had 13 points and 13 rebounds in the opening 24 minutes.
Notes: It was Howard's sixth game this season with at least 20 points and 20 rebounds. ... Heat point guard Mario Chalmers missed his first start of the season with a sprained left hand.