Parra was the first to go as he was sent to the Brewers in exchange for outfielder Mitch Haniger and left-hander Anthony Banda.
Though the Parra talks had been ongoing, the Prado deal with the Yankees, which netted Arizona slugging catcher Peter O'Brien and a player to be named or cash, came together closer to the 1 p.m. MT deadline.
Haniger, 23, was ranked as the eighth-best prospect in the Brewers' system by MLB.com and was hitting .255 with seven doubles, 10 homers and 34 RBIs at Double-A Huntsville. He missed some time this year due to a hyperextended elbow.
"We were very high on him when he was an amateur," D-backs GM Kevin Towers said. "Kind of profiles probably more as a corner outfielder, though, he has played center. Speed is probably the lowest grade that we have on him, but defender with a plus arm, plus power, plus hitter. A guy that will probably go to Double-A for us in Mobile, but a corner outfielder that we think could be a five- or six-hole-type hitter here in the very near future."
Banda, who turns 21 in a couple of weeks, has appeared in 20 games (14 starts) for Class A Wisconsin and was 6-6 with two saves and a 3.66 ERA.
"Banda is coming on pretty good," Brewers GM Doug Melvin said. "He's a 20-year-old left-hander who keeps getting better each time out. He's got a nice delivery, 89-91 [mph] but has got good command. Not a power guy, but he's a nice pitcher."
O'Brien, 24, was selected by the Yankees in the second round of the 2012 First-Year Player Draft and has put up monster power numbers in the Minor Leagues. Combined at Class A Tampa and Double-A Trenton this year, he hit .267 with 23 doubles, 33 homers and 70 RBIs.
Ranked as the ninth-best prospect in the Yankees' system by MLB.com, O'Brien was selected for this year's All-Star Futures Game.
The biggest question with O'Brien is with his defense and whether or not he can stick as a catcher or will need to be moved. In the Yankees' system, he spent time behind the plate, at first base, right field and third base.
Towers said the D-backs plan to use him as a catcher and they believe that catching instructor Bill Plummer can help him. O'Brien will start out at Mobile.
"O'Brien is probably one of the best offensive players in the Minor Leagues right now," Towers said. "He's going to be wearing the gear for us. Talked to him on the phone, he was excited about that. We think he's going to hit for average, we think he's going to drive in runs and our scouts believe that he can be an offensive catcher behind the plate, maybe of the [Evan] Gattis type."
O'Brien has hit 65 home runs in three seasons. Entering Thursday, he was tied for second overall in the Minors in extra-base hits (58), third in home runs, fourth in total bases (229) and ninth in slugging percentage (.593).
In addition to the players, the D-backs gained some much-needed payroll flexibility as they try to retool for 2015.
The D-backs did not have to send any money in either of the trades. That means that they will save on what Prado and Parra were left to make this year. In addition, the team is freed from the $22 million it owed Prado over the next two years.
Parra would have been eligible for salary arbitration this offseason and would likely have commanded a raise to the range of $6 million to $7 million. Going through a down year both at the plate and in the field, Parra became expendable with the emergence of outfielder David Peralta.
While the D-backs liked Prado, they also felt they had depth at third base with Jake Lamb, who is at Mobile, and Brandon Drury, who is at Class A Visalia.
The D-backs went into this year with a franchise-record $110 million payroll, and without moving some of their future obligations, it would have limited their ability to add pieces during the offseason.
"It gives us some flexibility and the ability to maybe do some more things this winter," Towers said. "To allocate those dollars more towards pitching and other needs."
The D-backs might not necessarily be done dealing either. Players can still be traded during August but need to clear waivers first. A player such as second baseman Aaron Hill, given his contract, would likely clear waivers and might be looked at by a contending club should they lose their second baseman to injury.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.