Midfielder Pallardo struck into the top corner from 20 yards on five minutes, and Keatings was equally accurate with his finish as he picked out the bottom corner with his left foot from inside the box soon after.
The Edinburgh club would have been further ahead had Craig McDowall not smartly denied Alim Ozturk and Danny Wilson as they survived until the break, despite Pallardo and Walker having reasonable opportunities.
Alloa briefly ruffled Hearts feathers as Spence's header against the run of play halved the deficit on 61 minutes and Calaum Jahraldo-Martin narrowly missed the target with a free kick as they teased an equaliser.
Walker quickly killed off any hopes of an Athletic comeback as he thrashed home from close range, and Paterson nodded Billy King's cross beyond McDowall in stoppage time to complete a comfortable evening's work.
Hearts move 16 points clear of Rangers, who have two games in hand, at the top of the table, while Alloa remain second from bottom and are now winless in 10 league games.