Guingamp had seen fellow Ligue 1 sides Paris Saint-Germain and Saint-Etienne book their places in the last four earlier in the week, but had to rely on Beauvue's set-piece in the second of two minutes' stoppage time to see off their lesser opponents.
Christophe Mandanne had fired Guingamp into the lead in the third minute after a scrappy sequence of play in the hosts' penalty box, but Christophe Gourmelon sent the home fans into raptures with a lobbed 22nd-minute equaliser.
The match looked destined for extra time until Beauvue posted his free-kick into the top left-hand corner, leaving goalkeeper Ivan Seznec stranded.
Thursday's earlier match between Brest and Auxerre did require additional time and it was the latter who prevailed after the tie went all the way to penalties.
Brest did not get off to the best start in the shootout, as Youssef Adnane was unsuccessful with their first attempt, but Thomas Fontaine's inability to convert his own spot-kick saw the scores levelled up at 2-2.
However, Frederic Sammartino stepped up to net the decisive penalty after Simon Falette had failed to find the net with his strike.
On Wednesday, PSG knocked out a lacklustre Monaco with a 2-0 victory at Parc des Princes.
David Luiz opened the scoring early on before Edinson Cavani doubled the advantage after the interval, with the latter also striking the post.
Saint-Etienne were the first to book their semi-final berth on Tuesday, but had to rely on a 4-3 penalty win to see off Boulogne, who had held their top-flight visitors to a 1-1 draw over 120 minutes.
