Justin Upton doubled leading off the 10th against Aaron Heilman (0-3) and scored on Miguel Montero's sacrifice fly to help the Diamondbacks take two of three in the series.
Third baseman Augie Ojeda and shortstop Stephen Drew made diving plays in the bottom of the ninth to keep the score tied.
After Santana struck out 10 in seven shutout innings, Wagner squandered a two-run lead in the ninth and screamed at himself several times while walking back to the dugout.
The left-hander also gave up a go-ahead homer to San Diego pinch-hitter Tony Clark in Sunday's 8-6 loss and a tying, three-run shot to Mark Reynolds on Wednesday night. The Mets recovered to win that one on Carlos Beltran's 13th-inning homer, ending a five-game skid.
Wagner's slump is coming at a bad time, however, and the velocity on his fastball was down noticeably Thursday. New York fell three games below .500 again, matching a season worst.
The last time Wagner blew three save chances in a row was 2000 when he squandered five straight for Houston.
Santana tossed three-hit ball, outpitching Arizona's Dan Haren in a marquee matchup. But it was the third time in Santana's 14 starts that his bullpen cost him a win, including two blown saves by Wagner.
The two-time Cy Young Award winner also has lost twice when allowing only one earned run.
Brandon Lyon (2-1) worked two scoreless innings for the win and the NL West leaders won for only the sixth time in 20 road games. The last time they had captured a series away from home was when they won two of three at San Diego from April 25-27.
Ramon Castro homered and David Wright hit an RBI double for the Mets. Fernando Tatis had a two-run single, but New York wasted excellent opportunities to extend its 4-0 cushion in the seventh and a two-run lead in the eighth.
Reynolds' two-run triple off Joe Smith cut it to 4-2 in the eighth.
Wagner was ahead 1-2 on Montero in the ninth before issuing a leadoff walk. Drew reached on a pinch-hit infield single and Chris Young's RBI double cut it to 4-3.
Ojeda walked, loading the bases, and Mets manager Willie Randolph huddled with his players on the mound. Orlando Hudson grounded into a force play at the plate and Castro could have had a double play at third, but he only looked toward first before deciding to hang onto the ball.
Conor Jackson then hit a high chopper to shortstop and beat the attempted double-play relay to first, tying it at 4.
Jose Reyes was on second in the bottom of the ninth when Ojeda made a backhand stab of Wright's sharp grounder and fired to first for the out.
With the bases loaded and two outs, Drew hit the dirt for a backhand stop of Damion Easley's grounder and tossed to second, where Hudson barely beat Carlos Delgado to the bag.
Notes: The Mets were waiting for results of an MRI exam on oft-injured LF Moises Alou (left calf), who said he thinks "the DL is a possibility - again." Alou just came off the disabled list Tuesday, but his calf stiffened up in his first game back. "I don't feel very good," Alou said. ... Ojeda started at SS for Arizona, giving Drew a rest. ... Wright is the only major leaguer to play every inning this season. ... Easley was hit by a pitch twice.
