Pernis parried away a drive by McCulloch and then intervened to prevent a Jelavic cross reaching Miller.
Whittaker fired straight at Pernis after being set-up by Miller as Rangers looked to double their advantage.
Murphy's shot was saved by Pernis but the ball cannoned back off Severin and found the net.
Rankin fired his spot-kick straight at Pernis, who saved well before Goodwillie lashed the ball to safety.
St Johnstone's hopes of a consolation goal were dashed by Pernis's save to deny Davidson moments before full-time.
Templeton unleashed a stinging left-footed drive from an angle inside the box that was pushed behind by Pernis.
Invincibile carved out a shot that bounced awkwardly in front of Pernis, the United keeper adjusting well to block.
County started the game strongly and Vigurs tested United goalkeeper Dusan Pernis with a low drive after eight minutes.
Davidson smacked a volley over the bar from 20 yards as the Perth side kept Pernis on his toes.
The big Falkirk striker was odds-on score but hit his effort straight at Dusan Pernis in the Dundee United goal.
Cox then forced Pernis into a save with a controlled shot from the edge of the box that lacked power.
Substitute Saunders spurned a great chance to extend 'Well's lead when he sent a free header wide of Pernis's goal.
Templeton teed up Kevin Kyle outside the box, but the Scotland striker blasted a shot well over Dusan Pernis' crossbar.
United's Scott Severin turned the ball into his own net after his keeper Dusan Pernis had saved a Jamie Murphy drive.
United were rattled and almost immediately conceded another, but Pernis did well to push clear a thundering 22-yard drive from Milsom.
Chances were few and far between before the hosts sprung a lightening attack, with Jamie Murphy forces a great save from Pernis.
Magennis was proving a handful with his powerful running and his low drive was turned round the post off the legs of Pernis.
We didn't create mega chances but if you look at Dusan Pernis, I don't think he's had a save to make the whole game.
The Steelmen took an early lead when Scott Severin sent the ball into his own net after Dusan Pernis had parried Jamie Murphy's drive.
Pernis produced a fine stop of his own to turn a Keith Lasley half-volley from the edge of the penalty box over the crossbar.
Hibs midfielder John Rankin saw his penalty saved by Dusan Pernis after Prince Buaben had been penalised for a clumsy challenge on Danny Galbraith.
St Johnstone went close from a Danny Grainger free-kick and a Marcus Haber header, both of which were saved by the impressive Dusan Pernis.
That chance gave the game a much-needed jolt and Riordan played a neat one-two with Lewis Stevenson before screwing a shot wide of Pernis's goal.
Pernis in the United goal only had one real save to make and that was an easy low take from a Djebbour shot from fourteen yards.
Ryan Jack threatened a quick response, but the Aberdeen midfielder's powerful drive from the edge of the box was blocked by Pernis at the near post.
Corcoran spurned a great chance to give County the lead five minutes before the break when he glanced a header wide of goal with Pernis stranded.
Mihael Kovacevic failed to deal with a Jody Morris cross, allowing Moon headed the ball into MacDonald's path and he rifled a volley past Dusan Pernis.
Jelavic robbed Scott Severin in the opening seconds of the second half and blasted a shot towards goal that forced goalkeeper Pernis to beat the ball away.
Falkirk showed their intent to get back into the game on 21 minutes, when Vitor Lima stung the palms of Dusan Pernis from just inside the box.
Pernis took a risk to leave his box and make a clearance, giving St Johnstone an opening, but the hosts failed to make anything of the opportunity.
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