Cole pitched seven strong innings to end a personal three-game losing streak, and added an RBI single as the Pirates beat the Washington Nationals 5-1.
Cole (5-3) turned in the best outing of his young career, allowing a run on two hits in his eighth career start.
"He was just aggressive. Doing a good job locating his fastball. Mixing his off-speed pitches," Martin said. "But, I mean, he's got that overpowering stuff. When he doesn't give too many free passes and he's able to throw strikes in good locations, he's a tough at-bat."
The right-hander struck out four, walked one and hit a batter.
"(The) hitters he did get behind, because he got behind six or seven hitters, he got them out," manager Clint Hurdle said. "He was able to pitch with good stuff tonight and that's why he got through seven in such an efficient manner."
Cole's effort eased the burden on a bullpen that will have to make do -- at least for now -- without Grilli, who was placed on the 15-day disabled list Tuesday with a right forearm strain and went back to Pittsburgh to be examined by team doctors.
Wilson Ramos homered for Washington, which had just three hits. The Nationals have lost five straight and 10 of 12.
"Really, the thing about us right now is we're a little snake bit," Washington's Jayson Werth said. "Things aren't going our way and we're not winning games. We need to find a way to win a game."
After allowing the homer to Ramos in the third, Cole retired 15 of the last 16 hitters he faced against a Washington team playing its first game in front of new hitting coach Rick Schu.
"I fell behind some guys and was still able to make pitches," Cole said. "You always kind of keep telling yourself you're only one pitch away. Never let yourself out of the at-bat."
Cole accumulated as many hits at the plate -- going 2 for 3 -- as he allowed.
"It's the middle part of their order. Let's just go ahead and put our best on it and see if we can put the game away," Hurdle said of using Melancon with a four-run lead.
Washington's Taylor Jordan (0-3) allowed five runs, four earned, in 7 2/3 innings in his fifth career start. Through seven innings he'd given up two earned runs on seven hits, all singles.
Pittsburgh broke on top 3-0 in the second. After Alvarez and Martin singled, Garrett Jones walked to load the bases with no outs. Neil Walker, in his first game back from the disabled list, grounded into a fielder's choice. Jones was out at second while Alvarez scored.
Jordy Mercer then hit a potential double-play grounder to third, but Ryan Zimmerman's throw was dropped by Anthony Rendon at second. All runners were safe as Martin scored. Cole then hit with runners on first and second and, after showing bunt, swung and grounded a single between third and short to score Walker.
"I feel for my guy because he should have only gave up one run," Nationals manager Davey Johnson said. "We made the error that gave them two more runs. He had pitched so good in the seventh. I was going take him out for the left-hander. But I thought he deserved the chance to win that ballgame."
Washington got a run back when Ramos led off the third with his fifth home run of the year, a shot to center just beyond the reach of a leaping Andrew McCutcheon.
The Pirates added some insurance with two outs in the eighth. After Alvarez homered to make it 4-1, Martin singled. He stole second, took third on a throwing error by catcher Ramos, and scored on a double by pinch-hitter Gaby Sanchez.
"That's who we are. That's what we are," Hurdle said. "We've got to get production from the top all the way down and do little things. We were able to do some good little things tonight."
To make room for Walker, who had been on the disabled list since July 7 with right side soreness, Pittsburgh designated veteran infielder Brandon Inge for assignment. Inge appeared in 50 games, hitting .181 with a homer and seven RBIs. . To take Grilli's roster spot, the Pirates will recall right-hander Vic Black from Triple-A Indianapolis, where he's 1-2 with 15 saves and a 2.31 ERA. . Johnson said LHP Ross Detwiler, on the DL since July 7, will meet with a back specialist in Los Angeles Wednesday regarding his strained lower-back muscle. . Schu had been serving as minor league hitting coordinator before being tabbed Monday to replace Rick Eckstein, who was fired. . Pittsburgh LHP Francisco Liriano (9-4, 2.44) opposes Stephen Strasburg (5-7, 2.97) Wednesday night.