It was the perfect way for Lakeside to bounce back from their heavy defeat at Paignton Saints the previous week, which was their first loss of the campaign.
The two Plymouth teams are now level on points in fifth and sixth spots in the South-West Division with four wins out of five.
The hosts took the lead after just five minutes on Saturday when Jake Anderson scored following a quick counterattack.
Plympton should have equalised on 25 minutes but they fired wide after beating the goalkeeper.
The Lakeside keeper then made a good save before the home side doubled their lead in first half injury-time when Jack Presland reacted quickly to tap in after a long-range shot had bounced off the far post.
Plympton came out fired up for the second half and had four good efforts to pull a goal back before they eventually did with nine minutes to go.
The game had got quite feisty in the second period but Lakeside managed to keep their composure in the closing stages to secure a hard-earned three points.
It was their second derby win of the season, having beaten Plymstock United 4-2 last month.
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