Lester's opening goal meant he is the first Chesterfield player for 80 years to score 20 goals in consecutive seasons.
His second strike meant that Vale were left with too much to do and, although Paul Marshall reduced the arrears, Chesterfield deserved their victory.
But it was a hard struggle for the home side against a team that packed the midfield and defended skilfully.
They even survived the loss of their keeper, Joe Anyon, who was stretchered off after a collision with Drew Talbot and his replacement, 18-year-old Chris Martin, did not let his team-mates down.
Martin could do nothing about Lester's two strikes though and Vale might have had a more profitable afternoon if Marc Richards had shown a better touch in front of goal in the ninth minute when he scuffed a close-range chance.
It was the best opening the visitors had and Chesterfield always looked likely to break through although they had to be patient as Vale closed down at every opportunity.
Lewis Montrose struck the bar with a 20-yard shot in the 50th minute but Martin was left exposed when Paul Edwards made a hash of clearing a cross from Talbot and Lester smashed an eight-yard shot into the top corner.
There was a touch of good fortune about his second in the 74th minute when his free-kick came back off the wall and his follow-up took a deflection to beat Martin inside his right-hand post.
Vale responded two minutes later when Marshall's free-kick from out on the right crept through a crowded area and sneaked past Tommy Lee and inside his right--hand post.
Lee made a good save when Marshall tried his luck from 20 yards but Lester was close to a hat-trick three minutes from time when his right-foot shot from 15 yards came back off a post.