Quick aside for some stuff I thought was interesting while looking at this:
The O's haven't even played a ton of close games in general; the 29 overall one-run games is the 5th fewest in the AL, and below the league average of 31+. If they could only (a) engineer more close games, and (b) continue their crazy success in them, then they could actually approach 90 wins.
Either the O's win a close one, or they lose - not surprising given the above records. The degree to which this has been true is a little staggering though; they've won by what seems like a reasonable 4 runs only twice all year, which is often as the team has been blown out by 12 runs.
Sixes have been somewhat lucky, as the team has also dominated when that has been the margin of victory (10-4). They've won as many times by exactly 6 runs as they have when coming out ahead by 4, 5, 7, 8, 9, etc. runs... combined.
There is something to be said for the bullpen having a lot to do with the team's success. Buck Showalter has done a nice job leveraging the better relievers, having Pedro Strop and Jim Johnson pitching in closer games while throwing Kevin Gregg out there in mop-up duty. In that way, if the O's are ahead by a little, they can keep that lead - and once the fall too far behind, it really doesn't matter how much more out of hand the game gets. For example;
Jim Johnson has one of the worse ERAs in the pen at 3.08, but over half of the runs he's allowed this season have come in two games (5 against the Twins in what turned out to be a 19-7 loss, and 6 against the A's that ended 14-9). Otherwise he's been a shutdown reliever coming in for high leverage innings. No pansy stuff either; 36 of his 39 entrances in save situations have been with leads of 1 or 2 runs, and he's actually come in to tie games more often than in games where the O's were ahead by 3 runs.
The opening act for JJ has usually been Pedro Strop and his 1.46 ERA. He generally appears in the 8th with a 1 or 2 run O's lead, and then passes that off to Johnson for the save. I wouldn't mind seeing him get his strike-out to walk ratio above 2, but the run prevention has been great (as evidences by his team best 3.0 pitching brWAR).
Beyond that, even when Strop and JJ have given up runs it's rarely mattered. A lot of that is fluky - Johnson comes in with a two-run lead and gives up one, but still gets the save. In fact, of the 7 games in which Strop gave up a run, the O's still went on to win 5 of them; and of the 8 games in which JJ gave up a run, the O's still won 6 of them.
On the other side, there's Kevin Gregg, who has the worst ERA in the pen for guys with at least 20 IP (3.99). He's pitched in 35 games; of those, the O's won 8 (three by 3 runs or more) and lost 27 (22 by 3 runs or more). Amusingly, of the 8 wins, in half Gregg only came in because the game went into extra innings. Generally speaking, the guy who's done the most regular damage to the team's run differential is the one being kept away from important games at all costs (the average leverage index when Gregg's entered a ballgame has been around 0.5).
The other top relievers - Darren O'Day and Troy Patton - are right there with Strop when it comes to pitching in close games (percent of appearances where the score differences was two or less: O'Day; 65%, Strop; 63%, Patton; 60%), but they tend to show up more with the game tied or the O's just behind. So that's a relatively deep stable of pitchers having very good years that are available to either turn slim leads into close wins or keep things tight enough for the O's to come back (for a close win).
Certainly other teams get the whole "use better pitchers at higher leverage times" thing, but perhaps the Orioles have more opportunities to use it to their advantage because of the in and out starting pitching (sometimes they're good and the top part of the pen can work, and sometimes they're really, really not, and then we get to see Captain Chaos). The O's have allowed 6+ runs in 36% of their games (compared to 31% as the Major League average), while also allowing 2 or fewer runs in 33% of their games (compared to 31% as the Major League average). And the team has taken advantage of those well pitched games, winning a higher than average share (95% versus 87% for all teams).
Another part of it is probably the offensive being below average, since that means fewer blow-outs in the O's favor (they're 16-20 in games decided by 5 or more runs). That makes it harder to get the run differential up since they don't run up the score as often as that gets done against them.
In any case, there's probably at least a little something the Orioles are doing that's helping them turn some middling overall stats into more wins than you'd expect. And it's hard to argue they haven't been very lucky on top of that. It would still be surprising to see them continue winning ~54% of their games going forward, but it's certainly fun while it lasts.
A lot has been made this year (including by me) about the Orioles' run differential (bad) not matching up with their actual record (good). The O's have been outscored by 45 runs, which would indicate that they should be more like 57-66 than 66-57 - and their other non-W-L stats back up that kind of view (below average offense, poor defense, OK pitching-staff). It's the wins and losses that count though, and the team has already banked enough of them - however they got them - that they're actually in position for a play-off spot.
The run differential thing is pretty weird though. The Orioles have absolutely dominated in close games; when the margin of victory has been one run, they're 23-6 (easily the best record in the Majors); and when the margin of victory has been two runs, they're 20-12. In all other games the team is just 24-39.