Leigh Bromby, Leeds' central defender, untidily pulled down Southend striker Lee Barnard.
And Barnard, the former Spurs prospect, stepped up to take the spot-kick himself. He drove the ball towards the top right-hand corner only for Higgs to take off and thrust out his left fist, turning it away from the net.
It was frustrating for Southend because they had produced the best chances of the game and deserved to be in front.
It was the Shrimpers' French connection which had Simon Grayson's side worried.
Striker Francis Laurent tried a sneaky shot from the right for the near post but again Higgs, a Wolves reserve last season, was equal to it, scrambling the ball away from his post.
Southend again should have taken the lead on 45 minutes with a sweeping move begun by Adam Barrett.
The ball flowed through Laurent for Franck Moussa to beat his man and curl over a perfect centre. For once he misjudged and was in no man's land as Anthony Grant swooped, only to rifle the ball over the bar from five yards.
Leeds' leading scorer Jermaine Beckford was back but was wild in his attempts to break the deadlock.
It was Robert Snodgrass who looked like being Leeds' star in the first half-hour but the talented Scot faded and was substituted.
Southend handed Leeds a 1-0 defeat in the corresponding game last season and after Barnard's hat-trick a week ago against Leyton Orient, they fancied a repeat.
But this Leeds team kept on right to the end and would have made it a magnificent seven wins out of seven to start their season if Beckford had not spurned a late chance from five yards.
Thanks to Ian Gibb from the Mail Online for this match report
Southend Utd: Mildenhall; Francis, M'Voto, Barrett, Herd; Grant (Scannell 80), Christophe, McCormack, Moussa; Laurent (Freedman 80), Barnard. Subs Unused: Walker, Sankofa, O'Keefe, Joyce, Sawyer.
Leeds: Higgs; Crowe (Michalik 48), Kisnorbo, Bromby, Hughes; Snodgrass (Kilkenny 75), Howson, Doyle, Johnson, Becchio (Grella 82), Beckford.
Subs Unused: Ankergren, Prutton, Robinson, Showunmi.
Referee: P Taylor (Hertfordshire).