The former Premiership striker used his lightening pace to put his team back on the play-off trail after two successive league losses.
Clear chances were scarce in the opening exchanges, although Boston's Brad Maylett and Dennis Lawrence, for the visitors, fired in shots which failed to trouble either keeper.
However in the 14th minute Boston went ahead when Joachim got in behind the Wrexham defence and raced onto a threaded pass from Jason Lee before rounding Michael Ingham and slotting home.
Wrexham tried to hit back and Mark Jones wasted a shooting chance when firing wild over the top after a short corner routine by Darren Ferguson and Dean Bennett.
Wrexham then enjoyed a good spell and started to spray around some neat passes with Ferguson and Matt Crowell at the heart of many of their brightest moments, but all too often the visitors' creativity founded on a solid home back line.
Just before the break, Boston almost doubled their lead but a 22-yard free-kick by Ian Ross was held at full stretch by Ingham.
In the 51st minute Boston again went close when Stewart Talbot's cross from the left landed at Lee's feet, but he was denied by a fine last-ditch tackle from Dave Bayliss.
Moments later Ingham had to save well as Lee headed down a free-kick by Ross.
But, on the hour, Wrexham drew level when Ferguson threaded a pass through from Lee McEvilly to pierce the home rearguard and fire under Michels Kuipers.
However Boston hit back with another moment of Joachim magic. The striker accepted a pass from Lee Canoville and left the defenders trailing in his wake before firing pass Ingham from just inside the area.
Boston had a let of on 71 minutes when Kuipers dashed out and appeared to upend McEvilly, but referee Paul Melin turned down Wrexham's penalty appeal.
Three minutes from time McEvilly was again in a shooting position, but this time Kuipers dived at full length to push the ball away to safety.
Only seconds from the final whistle Lawrence was denied by Alan White's brilliant header off the line.