The 2007 Diamondbacks were the last playoff team with a negative run differential and they won the NL West that year and, as you probably remember, the Rockies sneaked into the playoffs with the then one Wild Card spot after an eleven game winning streak in September and having to play a game 163 against the San Diego Padres.
Before game 163, the Rockies and Padres were only game back of the D’Backs for the division as each of them were 89-73 and the D’Backs went 90-72.
The D’backs had a run differential of -22. For comparison, the Rockies run differential was +102.
If you look at the team on Baseball Reference (you can right here), you’ll see that they really aren’t anything special. They didn’t have a regular position player with an OPS+ of 109 (shared by first baseman Conor Jackson and future Rockie Mark Reynolds). Their actual leader in OPS+ was pitcher Micah Owings, who had 4 homers, 15 RBI, and a .333/.349/.683 slash line in 64 plate appearances.
On the pitching front, they main thing they had going for them was 47 saves by Jose Valverde.
The Rockies had the last laugh, though, as the D’backs were swept by the Rockies in the NLCS.