Howard ended 3-for-5 with two RBI and Byrd also had three hits, including a homer, and three RBI for Philadelphia, which swept this three-game set from the struggling Braves. Mayberry had just one hit, but added three RBI for the Phillies, winners in seven of their last nine overall.
Cesar Hernandez, Wil Nieves, Chase Utley and Domonic Brown also had multi-hit games as Philadelphia unleashed a season-high 18 hits on Braves pitchers to record their first sweep in Atlanta since 2011.
Evan Gattis and Ryan Doumit each homered for the Braves, who have dropped seven of nine.
The Phillies got going in the first with two runs off Atlanta starter Aaron Harang (5-6). Byrd singled home the first run, and with the bases loaded Mayberry walked to force home the second.
Atlanta took a lead in the home half of the inning against Philadelphia starter Roberto Hernandez, as Gattis hit a two-run homer and Doumit later added a two-run single for a short-lived 4-2 lead.
Philadelphia took control in the second, putting together a five-run inning all with two outs. Utley singled home the first run of the inning and later scored on Howard's double. Howard later scored from third on Byrd's infield single to put the Phillies ahead 5-4. Later in the frame, Mayberry laced a two-run single to give Philadelphia three-run cushion.
The Phillies added another run in the fourth on Reid Brignac's bases-loaded walk that plated Utley. Then, after Doumit hit a homer to draw the Braves within 8-5, Howard added an RBI single in the fifth for another four-run lead.
Byrd capped the scoring with his solo homer in the eighth.
Hernandez (3-5) got the win despite yielding five runs on eight hits, with five walks and two strikeouts, over six innings.
Harang struggled and suffered the loss, surrendering nine runs -- eight earned -- on 13 hits over five innings. He struck out four and walked three, losing for the third time in seven starts (1-3).
Brown had three hits and scored twice and Nieves' three hits included a ninth- inning double when he appeared to injure his right quad and needed to leave the game.