Opponents Wrexham were never in the hunt after seeing defender Steve Evans sent off for kicking Drewe Broughton.
And Boston fully exploited the numerical advantage they had for almost 70 minutes with two goals from Broughton adding to a brace by Anthony Elding.
Neither side created any real chances in a largely dull opening spell. The only slight scare came on 11 minutes when Wrexham defender Evans had to clear from close to his own line following a downward header by Broughton from a Francis Green cross.
In the 19th minute Boston had another chance when Elding crossed from the right but Green blazed over from 10 yards.
However, the Pilgrims went ahead in the 22nd minute with a well-worked goal. Flowing play involving Green, Mark Greaves and Lee Canoville saw the latter cross for Elding to net from six yards.
Sixty seconds later Wrexham were reduced to 10 men when Evans got his marching orders for kicking out at Broughton whose initial foul cost him a booking.
Wrexham sought to hit back and created danger with a couple of set pieces, but the home rear guard held firm.
Boston went close again in the 42nd minute when Broughton burst down the right but saw a 15 yard drive bounce away off the bar.
Moments before the break Boston pressed again and Jason Kennedy drilled inches too high from long range.
Boston doubled their lead on 48 minutes when Tim Ryan crossed from the left and an unmarked Broughton side-footed in from eight yards.
Boston pressed again and twice Kennedy figured in key moments. First he broke down the right but was unable to find Broughton with a low cross. Then on 65 minutes he got into the Wrexham danger area but dragged a shot inches wide.
Little was seen of the Wrexham attack and Boston went three goals clear on 69 minutes when Broughton burst clear and drilled in from 16 yards via a deflection off the unlucky Danny Williams.
There was more joy for Boston in the 83rd minute when Elding rose to meet a David Rowson cross and his glancing header flew past keeper Mike Ingham.