Gillingham centre-back Egan put through his own net to end Newcastle's 203-minute goalless start to the new season.
Newcastle were largely unchallenged by the toothless hosts in a straightforward Capital One Cup second round victory, but Alan Pardew's men were almost as blunt in attack themselves.
Newcastle toiled into the third game of the season for their first goal of the new campaign: when it finally arrived none of the St James' Park men could claim credit.
Gabriel Obertan's dangerous low cross forced Egan to put through his own net, Newcastle finally off the mark after the 2-0 Manchester City defeat and a goalless draw at Aston Villa.
This unconvincing victory will do little to ease pressure on Pardew, yet to build a cohesive unit from his new-look squad.
Summer signing Siem de Jong made his full debut in Kent, but was largely ineffective playing off lone frontman Emmanuel Riviere.
Neither French striker Riviere nor Dutch playmaker De Jong seemed comfortable leading the line, but such was Newcastle's dominance it did no damage.
Yoan Gouffran was unable to break the deadlock in Saturday's clash at Villa, and the rearranged frontline fared little better at Gillingham.
Pardew will now hope his new batch of strikers come good in Premier League action against Crystal Palace this weekend.
The whole ground stood for an applause tribute to John Alder and Liam Sweeney in the 17th minute, the two Newcastle fans who died in the MH17 plane crash.
The two sets of fans had scant else to toast until that point, with Newcastle failing to hit the target in the first 20 minutes.
The visitors only came under one sole moment of panic in the entire first-half, and the assured captain Fabricio Coloccini saw that off easily enough.
Cody McDonald appealed for a penalty under the Argentine defender's challenge, but Coloccini timed his tackle perfectly to snuff out Gillingham's solitary attack of the half.
Newcastle took the lead through one of a clutch of half-chances: the visitors could claim credit for the approach, but not the finish.
Obertan and full debutant Rolando Aarons exploited the space behind Gillingham's wing-backs for the entire half.
Obertan forced Egan to concede from one such raid, thanks to a dangerous low cross.
Newcastle were so comfortable as to shrug off more than intermittent wasteful passing from Mehdi Abeid and De Jong.
The visitors were content to knock the ball around in front of Gillingham's two banks of four, and listlessly at that for the most part.
Gillingham for their part seemed just as indifferent to the situation, hamstrung somewhat by their ineffective 3-5-2 formation.
The second half opened just as tamely as the first, and it took a thunderbolt 25-yard blast from Massadio Haidara that rattled the crossbar to shake both teams to life.
Haidara cantered through Gillingham's static defence moments later, but this time the shot was scuffed wide.
De Jong ought to have sneaked in to double Newcastle's lead, but his lack of sharpness again shone through as he hung off and watched the chance drift by.
Gillingham manager Peter Taylor rung the changes for the last quarter, and finally the hosts found some bite.
Luke Norris hassled Tim Krul into a nervy clearance, before launching a rasping 20-yard drive the Dutchman had to turn over the bar.