The Eastleigh keeper got the slightest of touches to thwart Brayley in his attempt, and Alexis — the former Burton Albion midfielder — made no mistake in rolling the ball into an empty net from the edge of the box.
But the gallant Conference South side were never really out of it and capitalised on some poor Aldershot defending to level the score — James Taylor allowed time to control and poke the ball past keeper Dan Weir from close range after Neville Roach crossed.
Eastleigh's revival however, lasted just two minutes as Brayley started and finished a fine sweeping move to put the Shots back in front — first spraying the ball out wide to fellow striker Senior and then firmly heading home on meeting Senior's inviting cross back to him.
Weir then endeared himself to the Shots fans further by saving a dubious penalty from Ryan Ashford late in the half.
The visitors levelled once again ten minutes into the re-start as Chris Warren nipped past a napping Will Salmon to slot past Weir, only then for the Shots to regain the lead once again just two minutes later — Alexis, doing his chances of earning a contract no harm with a second.
Alexis was then denied a hat-trick by the offside flag late on, capping a lively debut.
SHOTS: Weir; Sulaman, Salmon (sub Milletti 81mins), Nurse (Scott 83), Jinadu, Winfield (Turrell 83), Field (Lee 48), Alexis, Senior (Crittenden 45), Brayley, Cook (McNamara 45).
Att: 574.
With thanks to the Aldershot News.