Wanderers raced into an early lead courtesy of superb 25-yard strike by Mark Davies and proceeded to dominate the opening exchanges but could not add to their advantage, while Lee Martin came closest to finding an Ipswich equaliser before the break.
Despite a pair of early second-half chances for Kevin Davies, Town were growing into the game and DJ Campbell levelled from the penalty spot when Tyrone Mears brought down Darryl Murphy.
That left Chopra to capitalise on some slack handling from Bolton goalkeeper Adam Bogdan and move Ipswich five points clear of the relegation zone following back-to-back wins.
Bolton headed into the match unbeaten in their first six games under Freedman - a post-war record for a new Wanderers manager, and his side were ahead by the sixth minute.
Mark Davies exchanged passes with Jay Spearing before unleashing a sublime shot that dipped into the top corner, leaving Stephen Henderson with no chance.
Marcus Alonso had an effort from distance deflected behind before Kevin Davies prodded wide as he stretched to meet a pull back from strike partner David Ngog, but Ipswich managed to see out the early storm without suffering any further damage.
Wanderers might have extended their lead on the stroke of half-time but Chris Eagles elected to shoot with Kevin Davies well placed.
Henderson produced a magnificent stop when Kevin Davies fired a volley goalwards from Mark Davies' cross in the 50th minute. The veteran striker was thwarted again moments later with a header from Keith Andrews' lofted ball.
Despite those opportunities, Bolton were unable to reproduce their earlier fluency and Ipswich drew level with 20 minutes to play.
Bradley Orr played the ball in to Murphy who cutely nutmegged Zat Knight before being brought down by Mears.
Bogdan guessed correctly but Campbell's spot kick nestled in the corner.
Ipswich now appeared the most likely winners and Bogdan saved well with his feet from Martin following good work from Jay Emmanuel-Thomas, who was introduced in place of Andy Drury 10 minutes into the second half.
Bolton substitute Jacob Butterfield cut in from the left to thrash narrowly wide but there would be late heartbreak for the hosts after Knight blocked Murphy's goalbound effort.
The resulting corner, taken by Martin, was half cleared and and when Bogdan failed to hold Orr's well-struck volley Chopra was on hand to finish.