The result leaves the Devils needing 10 points from their final four matches to overhaul Ipswich and finish in the top six.
The Devils visit Rye House on Bank Holiday Monday and then have home matches against Berwick and Scunthorpe before rounding off their league programme with a visit to Scunthorpe on Friday September 11.
Particularly pleasing for Plymouth was the performance of new signing Linus Eklof, who scored 10 (paid 11) points from five rides on his debut for the Devils.
Co-promoter Ashley Taylor said: “We have brought Linus into the side because we need a team capable of producing results at home and away in our remaining fixtures.
“The win over Newcastle was due to a good team effort all round and now our target is ten points from the 14 available to us.”
Plymouth: Kyle Newman 12+2 (5 rides), Morten Risager 8+3 (4), Jack Holder 12+2 (5), Todd Kurtz 7+1 (4), Ryan Fisher 9+1 (4). Reserves: Sam Simota 7 (3), Linus Eklof 10+1 (5).
Newcastle: Steve Worrall 3+1 (4), rider replacement for Lewis Kerr, Alex Davies 11 (5), Anton Rosen 3 (6), Ludvig Lindgren 6 (6). Reserves: Simon Nielsen 4 (5), Sam Chapman 0 (4).