The Mets had taken a 2-0 lead in top of the second but they quickly gave it back in the bottom of the frame, when the Diamondbacks scored six times.
After Niese (7-5) issued a bases-loaded walk to Henry Blanco and an RBI single to pitcher Josh Collmenter to tie the score, Bloomquist hit a squibber to the left of the mound, allowing Stephen Drew to come home with the go-ahead run.
Niese fielded the grounder but his throw to first sailed down the right field line, letting two more D-back runs come across.
Bloomquist went to third on the play and scored on Aaron Hill's sacrifice fly to complete the big frame.
Chris Young added a pair hits, including a two-run double, as the Diamondbacks evened their four-game series at one win apiece.
Collmenter (3-2) earned the triumph despite yielding five runs on seven hits over six innings.