The Valiants escaped early embarrassment when Adam Chambers provided a measured cross for Jason Demetriou, who swung but failed to connect with the ball after only 20 seconds.
Vale debutant Simon Richman posed the first real threat to Orient when he found space 20 yards from goal, firing a left footed shot that flew inches over the bar after 10 minutes.
The visitors were gifted a penalty after 25 minutes when minimal contact from Adam Eckersley on Jabo Ibehre forced the linesman to raise his flag.
Top-scorer Adam Boyd had no problem stepping up to the spot and smashed the ball hard and low to the goalkeeper's right to claim his 16th goal of the season a minute later.
Leyton Orient looked dangerous after the break and almost doubled their lead when Charlie Daniels' looping cross was met by Andy Barcham, but the resulting header failed to hit the target.
O's goalkeeper Glenn Morris kept his side in the game when he flew to the rescue twice to make superb saves from both Danny Whitaker and Richman in the 55th minute.
After gaining momentum throughout the second half, Vale finally got on the scoresheet in the 75th minute when Eckersley atoned for his earlier mistake by supplying Marc Richards with a long cross that he planted into Morris' bottom right corner from 12 yards.
The home side continued to thrive and could have taken the lead seven minutes from time when Kyle Perry latched onto Luke Rodgers' pass only to send his shot over the bar from close range.
Basement side Port Vale made it back-to-back wins at home right at the death when Morris spilled Whitaker's shot for David Howland to follow up and slam the ball into the roof of the net.