Alfie Rutherford put the home side ahead in the second half but battling City quickly equalised and then Cody Cooke struck in injury time to take home the points - watch match highlights here.
The same goalscoring duo helped Truro come from behind at Hemel Hempstead on Saturday and these three wins have lifted them to seventh in the Vanarama National League South standings.
Thrilled manager Lee Hodges said: “We came up against a strong side who were in excellent form going into the game. It was an extremely resilient performance where we had to put our bodies on the line and get our heads in where it hurt.
“We had to soak up a lot of pressure before hitting them with two breakaway goals and it just shows the character and determination that we have in the squad.
“It was the same on Saturday where we put in a real shift to beat Hemel Hempstead Town and now we sit here with three wins in a row which, at any level of the game, is a real achievement.
“We will celebrate it, because we deserve it, before getting our heads on the challenge that Whitehawk will present on Saturday as we start a run of home games.”
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