The Chilean took centre stage as Barca began 2014 in superb fashion at Camp Nou on Sunday, with Neymar surprisingly left on the substitutes bench despite being available after a one-match suspension.
Alexis opened the scoring with a measured side-footed effort and added two further goals in the second half, completing his hat-trick with a superb 25-yard free-kick.
Speaking after the game, head coach Martino admitted he could have chosen to utilise Brazil international Neymar from the start.
"It was between Alexis and Neymar," he said. "Alexis was in better condition and we have to pick one of the two. We tried to figure out who was in better condition to play."
Martino was glowing in his praise for forward Pedro, who notched his sixth goal in as many league matches when registering Barcelona's second, and midfielder Cesc Fabregas, another integral figue against Elche.
He added: "Pedro is a player that can win any manager over. He always has answers for the team. He's a player who can assist; he can score goals; he's generous with his team-mates. It's hard for us to leave him on the bench.
"We have a lot of intelligent players and Cesc is one of the best at interpreting the game. He knows when he should help his team-mates and he gives great passes; he always finds just the right space."
Barcelona's triumph saw them return to the top of La Liga, and Martino is confident the side will be even more effective when Lionel Messi makes his return from a near two-month lay-off with a hamstring problem.
"The best player in the world will have an impact on the team," he continued. "We'll be even better."
Barcelona face Getafe in the first leg of a Copa del Rey last-16 tie on Wednesday, before resuming league duties in a top-of-the-table clash at Atletico Madrid on Saturday.
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