Bedard (6-12) retired 17 straight batters in the gem, allowing only one runner to get as far as third base.
The veteran left-hander didn't issue a walk as the Pirates claimed the opener of a four-game set.
Jason Grilli and Chad Qualls each hurled a scoreless frame to complete the whitewash for the Pirates, who kept pace with the Atlanta Braves for the top spot in the National League wild card standings.
D-backs starter Wade Miley (12-7) took the loss despite allowing only one unearned run on six hits over six frames.
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