Ortiz (1-1) allowed six hits, struck out eight and walked four in his fourth start. The 24-year-old right-hander had a pair of no-decisions and a loss despite pitching with a lead in his previous starts.
Barry Bonds and Doug Mirabelli had two RBIs each for the Giants, who moved within 1½ games of Chicago in the NL wild-card race.
Robb Nen got three outs for his 29th save. He gave up an RBI single to Tony Phillips with two outs, then struck out Lenny Harris with two on.
John Olerud had two doubles and picked up two assists and a putout in the fifth when the Mets turned the eighth triple play in their history.
After Bonds doubled home two runs off starter Bobby Jones (7-7) to give the Giants a 4-3 lead, he moved up when Jeff Kent singled to left. Bonds probably should have been waved in, but was held at third by coach Ron Wotus.
J.T. Snow then hit a hard grounder to Olerud, who checked Bonds at third before throwing to second for the first out. Shortstop Rey Ordonez also looked Bonds back before throwing to first for out No. 2.
After Olerud got the return throw, he fired home to get a sliding Bonds, who appeared to get under catcher Todd Pratt's tag.
It was the Mets' first triple play since June 6, 1989, at Chicago, and the club's first at home sine Sept. 29, 1982, also against the Cubs.
The triple play could only temporarily save Jones, who was chased in the sixth after giving up consecutive doubles to Rey Sanchez and Doug Mirabelli that put the Giants ahead 5-3.
Willie Blair relieved Jones and allowed Marvin Benard's RBI single.
Jones was charged with six runs and 12 hits in five-plus innings. Nine of his final 13 batters got hits.
Olerud's two-out, two-run double gave the Mets a 2-0 lead in the third. Olerud, who entered the game leading the NL in batting at .340, has a 19-game hitting streak.
The Giants came right back with two runs in the fourth off Jones on Snow's RBI double and a run-scoring groundout by Mirabelli.
Ordonez gave the Mets a 3-2 lead in the fourth with a two-out RBI double.
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