Wood (3-2) allowed one run and five hits while striking out eight in 6 2/3 innings for his first win since April 27 at Miami. He has worked at least six innings in each of his seven starts this season.
"He's got it," Sveum said. "He's figured it out."
Wood earned his first win at Wrigley Field since July 1 when he beat Houston. Over his previous 12 starts at Wrigley, he was 0-7 with a 4.58 ERA.
Sveum added: Wood is "the best starter in baseball, pretty much" through the first part of the season.
Responded Wood: "That's a strong statement."
He had to be pretty close to beat Lynn and the Cardinals.
St. Louis' six-game winning streak was its longest since an eight-game run in July 2010, and Lynn was trying to be the National League's first six-game winner.
"That's a really good lineup," Wood said. "I was fortunate enough to be able to locate pitches and have good command tonight and keep them off balance and end up having a good game."
Carlos Marmol relieved Wood with two outs in the seventh and pitched 1 1/3 scoreless innings. In the eighth he allowed a single to Yadier Molina and walked Jon Jay before getting out of the inning by picking Molina off between second and third.
Molina stole second earlier in the inning, and Marmol stepped off the mound with the Cardinals catcher on second.
"I'm glad he made that mistake," said Marmol, who's had consecutive scoreless outings since allowing three runs in a loss to Cincinnati on Saturday.
Kevin Gregg pitched a scoreless ninth for his fifth save in five opportunities since signing with Chicago on April 15.
The Cubs have won two straight since dropping four in a row.
Lynn, meanwhile, pitched seven innings and gave up two runs and four hits while striking out eight. Last year, Lynn (5-1) went 6-0 to start the season, earning his sixth victory on May 7.
He might have matched that feat if not for Schierholtz's fourth-inning home run.
"You look back at it, you gave up two runs on one swing," Lynn said. "I got behind him and made him hit it and he put a good swing on it so you tip your cap there, but for the most part I threw the ball well. That was only one I wanted back."
The Cardinals took a 1-0 lead with no outs in the second inning when Allen Craig hit a 2-2 fastball into the left field bleachers for his second home run of the year. Craig, who hit 22 last season, has two in the Cardinals' last three games.
That was it for the St. Louis offense, which had scored 29 runs in its last four games.
"(Wood) made good pitches when he had to," Cardinals manager Mike Matheny said. "We couldn't capitalize on the mistakes."
There weren't too many mistakes from Wood. He left with the lead May 2 against San Diego, but lost after he and the bullpen couldn't hold a 2-0 lead in a 4-2 defeat.
Nothing like that happened Tuesday against Lynn and the Cardinals
"(Lynn is) a good pitcher. I mean, that whole club over there is outstanding," Wood said. "They've got good players, solid players, good staff and everything. It's a confidence booster for us to come in and take Game 1 from them."
Prior to Tuesday's game the Cardinals activated 1B Matt Adams from the 15-day disabled list. Adams was on the DL retroactive to April 22 with a right oblique strain and pinch-hit in the ninth, popping out to left. ... Cubs reliever Kyuji Fujikawa, on the DL since April 13 with a right forearm strain, was scheduled to pitch one inning on a rehab assignment for Double-A Tennessee, but rain shortened the game to five innings before he could appear. The Cubs said Fujikawa would pitch Wednesday instead. Earlier Tuesday, Sveum said if Fujikawa's appearance went well, he could join Chicago this weekend in Washington. ... Jose Oquendo returned to coaching third base for the Cardinals after missing Sunday's game to tend to family matters. Chris Maloney went back to first. ... Sveum said starter Scott Feldman is "fine" after leaving Monday's game in the eighth inning with a cramp in his right index finger. ... Wednesday's pitching matchup is the Cardinals' Jake Westbrook (2-1, 1.07) against the Cubs' Carlos Villanueva (1-2, 2.85).