In his three starts since joining the Angels' rotation in place of the injured Jered Weaver, Richards (2-0) has given up just two earned runs in 20 innings (0.90 ERA) and hasn't surrendered a run in 12 straight.
After strong performances from Richards and Santana, Scioscia said he still doesn't know how the rotation will shake out once Weaver returns.
Richards will be thinking about what his fate may be in the coming days, he said, but the 24-year-old knows he has done all he could to prove he belongs.
"I felt good. Fastball command was really the key for me today," Richards said. "I was throwing my four-seamer for strikes. I was throwing my sinker for strikes, showing them that I could throw the slider for a strike also. Just keeping guys off balance."
The shutout was the Angels' league-leading ninth of the season and gave them their seventh win in their past nine games. The back-to-back shutouts by Richards and Frieri on Sunday and Santana on Saturday were the first since the Angels (36-31) tossed consecutive shutouts May 1-2. The win also moved them to a season-best five games over .500.
Though he had very few of them, Richards' biggest scare came in the fifth inning, when he had a runner on first and one out. D-backs third baseman Josh Bell hit a screamer down the right-field line that was destined for extra bases, but Albert Pujols made a quick backhand stab to turn it into double play, saving Richards from potential damage.
"If that ball gets by him, that's at least first and third, maybe it's a double, one run in," Scioscia said. "To turn that double play just shows the caliber of player that Albert is. The defensive side, the offensive side, everything he does. It was a big play at the time, and it ended up getting bigger as time went on."
Pujols' production didn't come solely on defense, however, as he drove in what ended up being the winning run with his 10th home run of the year in the fourth inning.
The Angels would add some insurance in the seventh on a two-out double from Mike Trout that scored Peter Bourjos from second. Trout had been mired in a 1-for-20 slump before the hit.
Before Trout's RBI double, the Angels hadn't scored a run via anything but the home run in 35 2/3 innings. It also snapped the Angels' streak of 18 straight at-bats without a hit with runners in scoring position. After a 1-for-6 day with RISP, the Angels are 5-for-46 in those situations over the past six games.
In the third inning, the Angels had men on first and second with one out, and first and third with two outs, but couldn't score. They had men on first and second with two outs in the fourth, and couldn't score.
"We need to get our club offensively to put a little more pressure on teams than we have," Scioscia said. "In the past six games, we've scored 11 runs. We have to be better than that, and we are better than that."
But for the second straight game, Angels starters forced their counterpart to waste a strong outing. D-backs righty Ian Kennedy (5-7) went the distance, giving up just two runs on six hits in eight innings. It was his third quality start in his past four games and first complete game since Aug. 1.
Santana ruined a six-inning, two-run performance from Joe Saunders on Saturday night, and on Sunday, the hard luck belonged to Kennedy.
"The guy did a really good job against us," Kennedy said of Richards. "I was the second-best pitcher today. He was pretty dang good out there, he's got pretty good stuff."