A return to the top flight for the first time in 25 years for Coventry appeared a formality earlier in the season as they stormed clear at the top of the table.
But a run of two wins in nine games had allowed Middlesbrough to move two points clear at the top prior to Monday's clash.
Wright's own form reflected that of the Sky Blues as he had scored just twice since October.
The USA international refound his scoring touch at the perfect time for Lampard.
Wright tapped in Jack Rudoni's cross and then latched onto a long ball from goalkeeper Carl Rushworth to smash in a second either side of half-time.
Riley McGree briefly threatened a Boro fightback when he lashed in midway through the second half.
The visitors' six-game winning league run, though, was ended when Wright completed his hat-trick from the penalty spot.
Middlesbrough have a five-point cushion over third-placed Millwall, with only the top two automatically promoted to the riches of the Premier League.
Ipswich, however, are just seven points off the promotion places and have two games in hand on the top two.
