The Dodgers lead the NL in both fielding percentage and defensive efficiency rating (DER). DER simply says what % of balls in play are turned into outs. The following link at mlb.com has the fielding stats Sortable Team Stats.
It seems unusual that at team would lead its league in both categories. A team (or player) can have a high fiedling percentage but not get to that many balls. But that is not the case with the Dodgers. They must be getting to alot of balls and are fielding them cleanly. So how many runs are they saving with all these balls they catch that other teams don't and all these errors they don't make?
Using data from ESPN, the Dodgers have allowed 452 runs this year with 422 of them being earned. So they have 30 unearned runs. The league average is 40. So that makes the Dodgers 10 runs better than average.
Then ESPN shows that the Dodgers DIPS% is 107, meaning that their pitchers would have an ERA that is 7% higher than it actually is if they allowed a league average of hits on balls in play (they are , of course, better than average). With their actual ERA being 3.61, then their DIPS ERA is 3.86. So here their fielders save .25 runs per game (that is, if the pitchers have nothing to do with batting average on balls in play). The Dodgers have played 115 games, so this is an additional 28.75 runs scored. Adding the 10 in from fewer unearned runs gives us 38.75 runs. Since it usually takes about 10 runs to win one game, a rough estimate is that the Dodgers have won close to 4 games this year with their fielding.
On the other hand, Fan Graphs Team Fielding shows them to have just about average defense using more advanced metrics.