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.
"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."
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.
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.
Mario Bermejo's header halved the deficit before the break but they remain rooted to the foot of the standings.
