The Seagulls would have celebrated a fourth win in that run had it not been for the brilliance of Emiliano Martinez, who kept his 12th clean sheet of the season.
The Villa keeper defied Albion with a succession of fantastic saves as he frustrated Leandro Trossard, Joel Veltman, Dan Burn and Danny Welbeck as Brighton couldn't find the three points their performance merited at the AMEX Stadium.
Villa, meanwhile, welcomed Douglas Luiz to their starting XI as Dean Smith only made one change from last weekend’s victory over Arsenal.
Seagulls dominate early
Brighton started like a team who were on a five-game unbeaten streak, with Burn heading Trossard's angled ball in off target before they ought to have broken the deadlock after ten minutes.
Veltman swung over an inviting right-wing cross which Alexis Mac Allister met with a firm header seven yards out but it flew wide when anything on target would have beaten Martinez.
The Villa keeper had to dive low to his left to save Veltman's drive after the Dutchman cut inside and it took 20 minutes before the visitors offered a threat when Alzate was booked for a heavy challenge on Jack Grealish.
It had been an encouraging first half hour for Albion. Veltman had done such a good job marking Grealish that the Villa captain switched to the right in search of space to influence proceedings.
Martinez made another save when Neal Maupay tried to surprise him from a tight angle at his near post before producing an even better stop after a great move ended with Trossard forcing the Villa keeper to turn a shot heading for the top corner over the bar.
It was turning into a one-man show of defiance from Martinez with Burn left shaking his head in disbelief when he flung himself to his right to keep out the defender’s header which was heading inside the post. Without him, Albion would have been out of sight. They’d had 12 first-half shots, more than in any 45 minutes in their top-flight history.
Villa hadn't had one until Robert Sanchez was finally called upon early in the second half when Ross Barkley fired straight at him but almost immediately Martinez made another somewhat unconventional save, blocking Mac Allister’s 20-yarder which had taken a deflection off John McGinn with his knee.
Martinez was having an inspired night and he produced another save for his personal highlights reel to deny Veltman, who cut onto his left foot and unleashed a shot that was heading for the top corner until Martinez flung out a hand to divert it over.
Maupay was next to threaten after a mazy run opened up space but, under pressure from Tyrone Mings, he ran out of room when a pass inside might have picked out the unmarked Pascal Gross.
Albion brought on Welbeck for Maupay with 11 minutes remaining and he nearly scored with his first touch only to be denied once again by Martinez, who sprung to his left to push the ball away after Welbeck touched on Adam Lallana’s cross.
Welbeck could hardly believe it and his incredulous reaction rather summed up Albion's night. Martinez had proved to be an impenetrable barrier.