Broadfoot's error was instrumental in Aberdeen's first-half goal but he made amends by scoring in the closing minutes to give his side a share of the points.
St Mirren had the best of the early play and the Aberdeen defence found themselves under serious pressure in the opening minutes, particularly from Simon Lappin.
The only time that Chris Smith was troubled in the St Mirren goal in the first 20 minutes was when Darren Mackie closed him down after intercepting a bad back pass from Broadfoot.
At the other end Jamie Langfield did well to get across his goal and make a low save from a Broadfoot header at the back post.
On the half-hour Mark Lappin produced St Mirren's best chance up to that point, sending a header inches wide of the upright with goalkeeper Langfield beaten.
But the game soon twisted in favour of Aberdeen and another poorly judged back-pass from Broadfoot gave Stevie Crawford a clear shot on goal, which he blasted beyond Smith to make it 1-0.
Aberdeen relaxed noticably after the goal, and started to pass the ball about superbly and with confidence.
They had the ball in the back of the net again before the interval but it was disallowed for offside. However television replays showed that Darren Mackie was clearly onside from the superb Crawford through-ball, and had the Dons gone 2-0 up it would have been a different story.
In an eventful closing period of the first half Aberdeen's Zander Diamond kicked out at Hugh Murray and was lucky to stay on the pitch.
Meanwhile, John Potter sent a header just off target as the Buddies searched for a leveller.
In the second half chances were few and far between. Dons sub Ricky Foster pulled the ball wide of the target when given a great opportunity in front of goal ten minutes from time following a dreadful challenge on John Stewart by a St Mirren defender on the half-way line.
Meanwhile Billy Mehmet had the home fans on the edge of their seats in the closing minutes only to head just over the crossbar.
Just as all looked lost for St Mirren, Broadfoot made amends for the mistake that led to Aberdeen's first-half goal and struck confidently to square the match.