The O's belied their poor form this season that has produced only one win in the last 14 games.
They could have taken the lead inside the first 30 seconds. Matt Lockwood found Jabo Ibehre on the edge of the area and he skillfully turned former O's defender Alan White but then dragged his shot wide of the far post.
Notts County currently lie sixth in the League Two table and were keen to show they were no pushovers as they responded immediately with a well-worked move.
David Pipe crossed to Jason Lee and the former Nottingham Forest striker out-muscled Alton Thelwell to set up Ian Ross 16 yards from goal, but he crashed his first-time drive against the upright with goalkeeper Glyn Garner well beaten.
Orient heeded the warning and went close twice in quick succession in the sixth and seventh minutes.
Gary Alexander, who was a class act on the field all afternoon, played a cross-field ball to Shane Tudor. The former Cambridge United player cut inside and delivered a superb cross to Ibehre in the penalty box but his header was straight at goalkeeper Kevin Pilkington and a good chance went begging.
Tudor was again at the heart of the second opportunity as he crossed to the returning Craig Easton, but the former Scotland Under-21 International couldn't keep his header on target and flashed a disappointing effort wide of the mark.
The Magpies struggled to deal with Orient's movement and the pressure finally tolled on twelve minutes.
Easton's long ball was picked up by Justin Miller who crossed to Alexander. He beautifully cushioned the ball to Wayne Corden and the former Port Vale player buried his chance into the bottom corner from 15 yards which left Pilkington with no absolutely chance.
Ibehre did have chances either side of the half but couldn't convert either and was clearly lacking in confidence on a disappointing afternoon.
Miller booked Orient's place in the next round in the 58th minute from a Matt Lockwood corner. The former Ipswich player rose highest to finish his cross with a quality header from six yards.
Lawrie Dudfield grabbed the consolation goal in injury time to give the Magpies' supporters something to cheer about but they were well beaten on the day.