Blues boss David Moyes was looking to continue the momentum after scooping the Premiership Manager of the Month award for September and was boosted by Aussie midfield star Tim Cahill's swift return to fitness after injury.
It was a severely depleted Southampton outfit who visited the Premiership high-flyers. First-choice strike duo Kevin Phillips and James Beattie were both missing through injury, and influential playmaker Marian Parhars was also a notable absentee.
Leon Best and Dexter Blackstock, both 18, made their full debuts up front in their stead.
The Blues' start reflected their lofty position. With Thomas Gravesen pulling strings in midfield and the spritely Marcus Bent constantly searching for an opening, Everton looked far more likely to open the scoring in the early stages.
A superb move involving Gravesen and Bent nearly put Osman in the clear on the ten minute mark, but his surge was intercepted as he entered the area.
The two combined again majestically again on 15 minutes, but Bent's weak cross shot was easily claimed by Antti Niemi.
Blackstock almost had a debut goal for the Saints on 20 minutes when he met Anders Svensson's cross, but the header went over.
Some tenacious wing play from Cahill then set up Bent for the best chance of the game, but the former Leicester striker blasted over from 12 yards. Kevin Kilbane then fired a free-kick inches wide.
Five minutes before the break Cahill latched on to Osman's touch, but again the ball sailed over the crossbar. Everton were getting ever closer to breaking the deadlock.
Following the restart, a terrible mix-up between Niemi and Jelle Van Damme gave Bent an open goal, but the defender atoned for his error with a great clearance off the line. From the resulting corner Bent had another goalbound effort cleared.
Southampton fired back as a surging run from Neil McCann sent Best free, but the young striker's first touch let him down as the action flowed back and forth.
Alan Stubbs was then forced to make a supreme last-ditch interception as Best again surged on to McCann's inswinging centre as the visitors began to take charge.
The visitors consolidated their grip on the midfield battle when the took off the tiring Best for midfielder Paul Telfer.
In the meantime Bent saw yet another chance go begging on 66 minutes, hitting a weak shot straight at Niemi from a tight angle.
Everton came agonisingly close again, on 73 minutes, as a Bent centre somehow evaded Osman and Cahill on the goal-line. Again the move was engineered by some wonderfully dynamic play from Gravesen.
With the Goodison crowd becoming restless Moyes went for broke bringing on strike duo Duncan Ferguson and James McFadden and the last-gasp goal duly arrived through youngster Osman, who swept the ball home from ten yards.
Man of the Match: Thomas Gravesen - Was at the heart of all of Everton's best efforts and drove his side on towards another hard-won three points.