The Rangers full-back grabbed the opener to ease the pressure on George Burley's shoulders just days after the national team boss claimed he was a player of "limited ability."
Barry Robson doubled the advantage with the rebound from a saved James McFadden penalty before skipper Stephen McManus was dismissed and Eidur Gudjohnsen netted from the spot to set up a tense finale.
Burley was forced to endure a difficult three days following the defeat in Macedonia with most of the criticism aimed at him personally.
Even so, he opted for a positive 4-3-3 formation and demonstrated he was not afraid to make some bold decisions in a bid to kick-start the campaign.
Kenny Miller and Graham Alexander were both fit enough to be named in the 18-man squad, after suffering knocks at the weekend, but were dropped to the bench along with Paul Hartley.
In came Broadfoot for his maiden international outing, while Kris Commons made his first start and Shaun Maloney was also drafted into the starting line-up.
A cool, crisp evening was far more suited to the Scots following the searing heat of Skopje and Burley was well aware there would be no excuses this time.
He was out of his dug-out within minutes of kick-off, urging his team forward, and they obliged.
Broadfoot delivered a cross from the right to Darren Fletcher but the Manchester United midfielder was denied the header by a timely clearance from Kristjan Sigurdsson.
At the other end Aaron Gunnarsson played a one-two with Birkir Saevarsson before unleashing a powerful angled drive that Craig Gordon did well to punch to safety.
The home nation continued to press and Gunnarsson supplied the cross and Heidar Helguson saw his header flash wide.
Gary Caldwell then made an excellent block to deny Helguson a shot before the ball broke to Gudjohnsen, who smashed over from close range.
Instead it was Scotland who had the net bulging with 19 minutes gone when Broadfoot met a Robson corner and steered home the opener at the near post from a few yards out.
Scotland could have added to their lead when Maloney swept the ball into the path of McFadden as he bore down on goal but Sigurdsson cleared before the Birmingham forward could unleash the shot.
With half-time approaching skipper McManus reacted quickly to clear off the line and deny Portsmouth's Hermann Hreidarsson the equaliser for the home nation.
Iceland had the bulk of possession after the restart as they attempted to haul themselves back into the tie but they found themselves with an even bigger task when Scotland added to their lead after 59 minutes.
McFadden was hauled down in the box by Sigurdsson as he chased a Fletcher free-kick and the referee immediately pointed to the penalty spot.
McFadden stepped up for the spot-kick himself and goalkeeper Kjartan Sturluson managed to block.
The taker and Robson both pounced on the rebound, with the Celtic midfielder appearing to have the last touch to prod over the line.
Just when it looked like they would cruise to victory, Scotland suffered a double setback when McManus was sent-off for deliberate handball and Iceland were awarded a penalty of their own.
Emil Hallfredsson delivered the cross intended for Helguson but McManus intercepted the move to push the ball out of play with his hand and the defender - 26th today - was a given a card he did not want.
Gudjohnsen then converted with ease from the spot when he rifled confidently past Gordon with 76 minutes on the clock.
There was then a late scare when a thunderous Helguson shot cannoned off Caldwell but 10-man Scotland held on for a much-needed win to maintain their 100% record against the host nation.