Wood (10-9) gave up three hits, walked four and hit a batter while striking out four in his eighth start for the Dodgers since coming over in a trade from Atlanta.
Crawford's RBI double in the fourth was enough for Los Angeles to win for the 10th time in 12 games and improve to a season-high 19 games over .500.
Kenley Jansen got the last three outs for his 29th save in 31 chances.
Tyson Ross (10-10) gave up a run and five hits in six innings. He walked two and struck out three.
Pederson added an RBI single in the eighth.
It was the second straight solid start for Wood, although he was on the losing end of the no-hitter by the Cubs' Jack Arrieta's no-hitter last Sunday. Wood gave up two runs in six innings of that game.
In his last three outings, Wood has allowed three runs in 18 2/3 innings.
The Padres were shut out for a major league-high 17th time this season, just two fewer than they had last year. San Diego had seven hits in its last two games against the Dodgers.
The Padres had the tying run at second in the seventh, after Wil Myers walked and advanced on Austin Hedges' sacrifice bunt. But Clint Barmes struck out, and after pinch-hitter Melvin Upton Jr. walked, Yangervis Solarte flied out to right field.
Matt Kemp led off the sixth inning with a single, but was picked off first by Wood when Kemp went back standing up. Kemp, who had two of the Padres' three hits, was originally ruled safe. But the call was overturned after a review of 1 minute, 46 seconds.
The Dodgers took a 1-0 lead when Andre Either, who had three hits, opened the fourth with his second double off Ross. Crawford followed with a ground-rule double which one-hopped into the right-field seats.
Ross wiggled from a second-inning jam when the Dodgers loaded the bases with one out. But he struck out Wood and got Jimmy Rollins to ground out.
PADRES: RHP Josh Johnson was to meet with team doctors after shutting down his minor league rehab stint on Friday after just four pitches. Johnson felt pain in his right elbow, which has undergone two Tommy John surgeries. ... RHP Brandon Maurer (right shoulder) has ceased throwing as the team decides his next step. ... 1B Yonder Alonso(back) could return by the end of the homestead. ... RHP Shawn Kelley (right forearm) has yet to resume throwing.
DODGERS: OF Either returned to the starting lineup for the first time since fouling a ball off his right knee on Wednesday.
Dodgers: LHP Brett Anderson (8- 8, 3. 43) faces the Padres to cap the four-game series. Anderson leads the majors with a 67.1 ground-ball percentage. He's pitched to a 5-4 record and a 2.67 ERA in 12 road starts this season.
Padres: RHP Andrew Cashner (5-13, 4.15 ) goes against the Dodgers for the fourth time this season. He's still seeking his first win, losing twice and getting a no-decision. Overall, Cashner has dropped three of his last four decisions.