Republic of Ireland striker Hunt converted from close range in the 17th minute after a well-worked corner before Harte killed off the game with a brilliant free-kick 10 minutes from time.
The impressive result completed a successful week for the Royals, who tied manager Brian McDermott to a new contract despite interest from Premier League side Wolves.
After failing to create any clear-cut opportunities in the opening half, Boro tested visiting goalkeeper Adam Federici on numerous occasions in the second but could not find a way back into the game.
Reading continued their promotion charge after their fifth consecutive clean sheet, while Tony Mowbray's side slipped to their third home league defeat of the campaign.
After a scrappy start, Reading started to take control and broke the deadlock from their first corner.
A smart interchange between Harte and Jimmy Kebe led to the former delivering into the box toward Alex Pearce and, after the defender guided the ball back across the face of the goal, Hunt was in the right place to convert from six yards via the underside of the bar.
Lukas Jutkiewicz had a shot blocked by Pearce and top-scorer Marvin Emnes fired wide as Middlesbrough struggled to create any clear-cut chances.
In-form striker Jason Roberts' tame effort from a McAnuff cross was blocked by Julio Arca, who ended the half by striking wide from 25 yards.
Boro started brightly after the interval and Rhys Williams was the first to work Federici with a looping header.
Arca's fierce strike just flew over the bar before Federici was grateful to grasp a Williams effort from 25 yards.
At the other end, Roberts broke clear of the last defender and should have put Reading 2-0 ahead, only to see Jason Steele's outstretched boot deny him his fourth goal in five games since his January move from Blackburn.
The miss seemed to lift Boro and Jutkiewicz had two chances in as many minutes to draw his side level. The former Coventry striker shot straight at Federici before bringing the best out of the Australian keeper with a header.
Despite late Boro pressure, Reading extended their lead and killed off the game through deadball specialist Harte.
The former Leeds defender curled a superb 25-yard free-kick into the top corner after 80 minutes.
Reading, who were unlucky not to be awarded a last-minute penalty when McAnuff appeared to be pulled down in the box, held on to claim their first win at The Riverside since 2008.