Chennaiyin lost their 100 per cent record in the newly formed league when they were consigned to a 4-1 defeat by Delhi Dynamos on Saturday, but they responded in style three days later.
Elano had scored in each of his first three games for Marco Materazzi's side and the former Brazil midfielder added another two goals to his tally, as well as setting up another two, as Chennaiyin ran riot at the Jawaharlal Nehru Stadium.
The 33-year-old set the ball rolling when he scored from the penalty spot just nine minutes in after Manuel Friedrich had upended John Stiven Mendoza.
Jeje Lalpekhlua then latched onto an Elano pass to double the home side's lead with a clinical finish and Colombian striker Mendoza struck twice in the space of three minutes just before half-time as Peter Reid's side were put to the sword.
The irrepressible Elano added a fifth goal 69 minutes in to add to the visitors' misery and although Syed Rahim Nabi pulled a goal back two minutes from time, that was never going to take the gloss off a resounding victory for Materazzi's men as Mumbai were left to reflect on a third defeat from their first four games.
Second-placed Chennaiyin are now just two points behind Atletico de Kolkata after the leaders were held to a 1-1 draw at home to Kerala Blasters on Sunday.
Assistant coach Angel Diaz Barrachina took charge of Atletico with Antonio Lopez serving a four-match ban due to an altercation with FC Goa midfielder Robert Pires, but he was unable to inspire another victory for the leaders.
Baljit Sahni put Atletico in front 22 minutes in with a fine finish after being set up by Borja Fernandez, but Kerala hit back to claim their first point courtesy of Canadian striker Iain Hume's second goal in as many games.
Goa have now picked up only one point from their first four games after they were beaten 2-0 at Pune City on Sunday, with David Trezeguet and Konstantinos Katsouranis scoring their first goals for the home side to secure their first win.
Delhi Dynamos and NorthEast United played out a goalless draw in the only game to be played on Wednesday.
