Andy Sandell marked his 50th appearance for the Shots by curling in a superb left-footed free-kick only for Brett Pitman to equalise from the penalty spot.
But an injury-ravaged Bournemouth, who could only name six substitutes, succumbed late on to Straker's inventive effort before Warren Cummings was sent off.
Aldershot started brightly and the goal came after Marlon Jackson, on loan from Bristol City, displayed some electrifying pace and ran at the Cherries' defence after 21 minutes.
The Shots winger was brought down on the edge of the area by Ryan Garry, allowing Sandell to step up and dispatch his free-kick into the top corner.
But Aldershot's Chris Blackburn was penalised for pulling down Steve Fletcher in the box after 61 minutes, allowing top-scorer Pitman to score his 14th league goal of the season.
Bournemouth could not hold on though and substitute Straker won the game late on as tempers flared with Cummings and un-used Shots substitute Clark Masters seeing red in the dying minutes for their part in a melee.