CINCINNATI — Rookie Drew Stubbs took a poke at the fastball and missed, providing the perfect ending.

The Los Angeles Dodgers struck out 20 batters on Sunday, their highest total in 37 years. Matt Kemp provided just enough offense with a solo homer and a sacrifice fly, and the overpowering pitching staff did the rest in a 3-2, 12-inning victory over the Cincinnati Reds.

‘‘They’ve got some powerful arms over there,’’ manager Dusty Baker said. ‘‘I don’t know how many strikeouts we had, but we had a bunch.’’

They came so fast that it was easy to lose track.

The Dodgers hadn’t struck out 20 batters since Aug. 8, 1972, when they fanned 22 Reds during a 19-inning game at Riverfront Stadium. This one was seven innings shorter, making the total much more impressive.

Left-hander Clayton Kershaw struck out 11 in seven innings, and five relievers kept it going. They struck out at least two batters in each of the ninth, 10th, 11th and 12th innings.

‘‘They’ve been awesome the whole year,’’ Kershaw said of the bullpen, which leads the majors in wins and earned run average. ‘‘They’ve picked up everybody. They’ve been the rock of this team.’’

The NL West leaders took two of three from the Reds over the weekend, extending their lead over Colorado. No surprise there — the Dodgers are 22-4 against the Reds since 2006, their best mark against any NL team, according to STATS LLC.

The bullpen had a big hand in both wins, throwing 11 2-3 scoreless innings.

‘‘These guys are taking this opportunity and certainly giving us the opportunity to do something special,’’ manager Joe Torre said.

They made it easy on an offense that had trouble coming up with a decisive hit.

The Dodgers wasted scoring chances in the eighth, ninth and 11th innings before finally breaking through against closer Francisco Cordero (2-4), who loaded the bases with a walk to Manny Ramirez, a double by Juan Castro and an intentional walk to Andre Ethier with one out.

Kemp’s fly to the warning track in center snapped the tie and gave the Dodgers their seventh victory in the last 10 games overall.

‘‘Scrappy teams with playoff experience usually find a way,’’ Reds starter Bronson Arroyo said.

James McDonald (4-3) pitched a perfect 11th inning, and Jonathan Broxton escaped a two-on threat in the 12th for his 29th save in 34 chances. All three of hits outs came on strikeouts.

The only disappointment for LA: Kershaw couldn’t snap his astounding streak of futility. The left-hander hasn’t won a game since July 18, going 0-2 in his last eight starts despite pitching well — a 2.91 ERA during that stretch.

The reason: No runs.

The Dodgers have scored an average of less than two runs during that stretch, giving the 21-year-old pitcher no margin for error. He tried to fix the problem single-handedly on Sunday, driving in a run with a single in the fifth inning. Kemp also had a solo homer off Arroyo, who lasted 7 1-3 innings.

At least the Dodgers won this one. In Kershaw’s last seven starts, they lost.

‘‘When the team wins, you feel better about your game, really,’’ Kershaw said.

Kershaw allowed only four hits. His one mistake came in the second, when Darnell McDonald hit his first major league homer for a 2-0 lead.

Torre tried to give the slumping Ramirez a day off, leaving him out of the starting lineup. Ramirez hit a two-run homer during an 11-4 win on Saturday, but hasn’t done much for the past couple of weeks. He has only two extra-base hits in his last 13 games.

He pinch-hit for Kershaw in the eighth inning and popped out, then stayed in the game in left field. He later had an infield single and the leadoff walk that started the winning rally.

NOTES: The Dodgers acquired INF Ronnie Belliard from Washington after the game. … Ramirez is 1 for 4 off the bench this season, including his first career pinch-hit grand slam against the Reds on July 22 at Dodger Stadium. … It was Kershaw’s third double-digit strikeout game of the season. … The Reds play a day-night doubleheader against the Pirates on Monday, making up a game rained out on April 10. The Pirates and Reds last played a doubleheader in Cincinnati on July 2, 1993 at Riverfront Stadium, splitting the two games. … Joey Votto struck out four times.

Reds’ boxscore

Sunday’s Game

Dodgers 3, Reds 2, 12 innings

Los Angeles Cincinnati

ab r h bi ab r h bi

Furcal ss 5 0 0 0 Stubbs cf 6 0 2 0

Pierre lf 4 0 1 0 Janish ss 5 0 2 0

Sherrill p 0 0 0 0 Votto 1b 5 0 0 0

Troncs p 0 0 0 0 BPhllps 2b 5 0 1 0

Loretta ph 1 0 1 0 Rolen 3b 4 1 2 0

Kuo p 0 0 0 0 Gomes rf 3 0 0 0

JCastro 2b 1 0 1 0 Rhodes p 0 0 0 0

Ethier rf 5 0 1 0 Masset p 0 0 0 0

Kemp cf 4 1 1 2 L.Nix ph 1 0 0 0

Blake 3b 5 1 1 0 Burton p 0 0 0 0

Loney 1b 4 0 1 0 Sutton ph 0 0 0 0

RMartn c 5 0 1 0 Corder p 0 0 0 0

Hudson 2b 5 0 1 0 ARosls ph 0 0 0 0

JMcDnl p 0 0 0 0 DMcDn lf 4 1 1 2

Broxtn p 0 0 0 0 CMiller c 4 0 0 0

Kershw p 2 0 1 1 HBaily pr 0 0 0 0

MRmrz ph-lf 2 1 1 0 Arroyo p 2 0 0 0

Balentn rf 3 0 0 0

Totals 43 3 11 3 Totals 42 2 8 2

Los Angeles 000 020 000 001 — 3

Cincinnati 020 000 000 000 — 2

DP—Cincinnati 3. LOB—Los Angeles 11, Cincinnati 8. 2B—J.Castro (4), Ethier (35). HR—Kemp (21), D.McDonald (1). SB—Ethier (6), B.Phillips (21). CS—Rolen (1). SF—Kemp.

IP H R ER BB SO

Los Angeles

Kershaw 7 4 2 2 2 11

Sherrill 1 2 0 0 0 0

Troncoso 1 0 0 0 0 2

Kuo 1 1 0 0 0 2

Ja.McDonald W,4-3 1 1 0 0 0 2

Broxton S,29-34 1 0 0 0 2 3

Cincinnati

Arroyo 7 1-3 6 2 2 2 3

Rhodes 1-3 0 0 0 0 0

Masset 1 1-3 1 0 0 1 1

Burton 2 3 0 0 1 0

Cordero L,2-4 1 1 1 1 2 0

PB—R.Martin. Umpires—Home, Eric Cooper; First, Mike Reilly; Second, Chuck Meriwether; Third, Laz Diaz. T—3:54. A—26,091 (42,319).