Carolina dominated Baltimore in every facet of the game and took advantage of several Ravens miscues.
"We needed that," Panthers safety Mike Adams said. "Now, we just have to keep this thing going."
Newton completed 21-of-29 passes for 219 yards with a pair of touchdowns. He also ran for a 12-yard score that provided a 33-14 lead with just under 10 minutes left in the game.
Moore caught five passes for 90 yards and also had an impressive 28-yard scamper that set up the Panthers' third touchdown.
Running back Christian McCaffrey also was effective against a Baltimore defense that entered the game ranked first in the league for fewest yards (280.6) and fewest points (14.4) allowed. He finished with 45 yards on 14 carries with a touchdown. He also caught a 6-yard touchdown pass.
The win keeps the Panthers (5-2) in the thick of the race for the NFC South title with New Orleans.
"We found our rhythm and played as well as we have all year," Carolina tight end Greg Olsen said.
Baltimore quarterback Joe Flacco had the worst performance of his season, completing just 22-of-39 passes for 192 yards with two interceptions -- a passer rating of 56.8. Flacco was benched late in the fourth quarter for Lamar Jackson, who threw a 26-yard touchdown pass to fellow rookie Hayden Hurst to round out the scoring.
After Alex Collins gave the Ravens a 7-0 lead on a 14-yard run with 7:50 left in the first quarter, the Panthers scored 27 consecutive points.
"On our part, we just didn't have it," Ravens head coach John Harbaugh said. "We weren't there in terms of what we needed to do -- coaching, planning, anything else. It starts with me. It's on my shoulders completely. I'll take responsibility for it and it's one we have to put behind us and look forward to the next game."
Both teams were 6-of-12 on third down.
The Ravens were playing their fifth road game in eight weeks and fell to 4-4. Baltimore was hampered by several mental and physical mistakes, including an illegal block by running back Javorius Allen that nullified a big gain on a reverse to Chris Moore.
Baltimore appeared to extend a drive with a fake punt, but the first down was brought back by an illegal shift. On third-and-one from their own 9-yard line, Jackson lined up behind the center, faked a handoff and had Willie Snead wide open downfield for a potential big gain, but he threw the pass directly into the turf.
A fumble by Collins on his own 10-yard line set up the Panthers' second touchdown for a 14-7 lead in the second quarter.
Snead had two pass interference penalties in the second quarter.
Meanwhile, the Ravens' usually stout defense could not get off the field. The Panthers drove 99 yards and took a 21-7 lead when McCaffrey caught a tipped pass in the end zone with 3:45 remaining in the half.
Baltimore finally stopped the bleeding on a 9-yard touchdown pass from Flacco to Allen with 10 seconds left in the third quarter that cut the margin to 27-14. The Panthers responded on the ensuing drive with a 12-yard touchdown run by Newton.
The Ravens now face a critical matchup with the Pittsburgh Steelers in Week 9. A loss would be devastating to Baltimore's playoff chances.
"We're disappointed," Flacco said. "This is obviously going to be a tough test for us to see what we're made of."