Swede Zlatan Ibrahimovic dropped out with an ankle problem and France striker Henry made the most of his opportunity, having watched the last three matches from the bench.
He netted a fortuitous free-kick in the 29th minute after Andres Iniesta had opened the scoring at the Nou Camp.
Rafael Marquez made it 3-0 with a superb curling free-kick in the 34th before youth team midfielder Thiago came off the bench to add the fourth goal near the end.
"We were comfortable but we weren't brilliant. We lacked rhythm," Barcelona coach Pep Guardiola told reporters. "To win titles we need to play a little better than this."
The leaders have 58 points from 23 games but second-placed Real Madrid can cut the gap on Sunday when they host Villarreal.
Nine-man Sevilla climbed to fourth on 42 points with a 3-1 victory at Real Mallorca, who lost their perfect home record.
Mallorca slipped to sixth with 37, one behind Deportivo La Coruna, who beat bottom club Xerez 2-1 earlier on Saturday.
Barca's extensive injury list deprived them of Ibrahimovic, Xavi and Daniel Alves but they quickly shrugged off doubts that last weekend's first defeat of the season at Atletico Madrid had done any lasting damage.
The match was only seven minutes old when Marquez's long ball caught out the visiting defence and Iniesta pounced to score his first goal since knocking Chelsea out of the Champions League in last season's semi-finals.
Henry netted only his third goal of the campaign when his free kick went through the wall and Marquez then bettered it as the Mexican's effort shaped over the wall and in off the post.
Barca wrapped up a comfortable win when Lionel Messi set up Thiago for his first goal with a deflected shot six minutes from time.
RED CARDS
Sevilla and Real Mallorca had Alvaro Negredo and Ivan Ramis sent off in separate first-half incidents at the Ono Estadi but the visitors responded better to the setback.
Mario Suarez gave Mallorca the lead after five minutes but Jesus Navas equalised before the break after a defensive error.
An Ivica Dragutinovic free kick in the 57th followed soon after by a Diego Perotti goal sealed the victory for the Andalusians who had Didier Zokora sent off at the end.
Xerez's search for a first away win in the top flight got off to a bad start at the Riazor where they conceded a penalty after three minutes which Mexican forward Andres Guardado converted.
Visiting coach Nestor Gorosito was sent to the stands for protesting and in the seventh minute Depor striker Riki broke clear to double the lead.
Mario Bermejo's header halved the deficit before the break but they remain rooted to the foot of the standings.
