The Gladiators dispensed of high-flying Marske United, with Alex Byrne scoring a brace either side of Reece Kendall’s goal.
Boss Paul Phillips said: “We seem to make a habit of making things more difficult for ourselves, we did it against Rushden in an earlier round.
“For 70 minutes we were dominant, even when they scored early in the game. Our tempo was good and we could have scored a couple more than the two we got in the first half.
“Late on Marske threw the kitchen sink at us but we stood up to it but on the whole I think we deserved to win by more.
“The biggest thing is to get through, the game was a great advert for non league football in the first half.
“It was important for everyone at the club to win the game, now we’ve got a good game with York to look forward to, but we’ll look at that after we’ve got the two important league games out of the way.”
Lancaster were 3-1 winners away at another East Division high-flier, Liversedge.
Rhys Turner scored two after Glenn Steel’s opener.
Dan Cockerline's goal was enough to secure Nantwich Town a 1-0 win away at Premier Division rivals Whitby Town.
The trio join Radcliffe and Morpeth Town in the third round of the FA Trophy.
Unfortunately, Stalybridge Celtic couldn’t join them, as they lost to still reigning NPL champions Farsley 1-0.
Ashton host Guiseley and Marine travel to Bradford Park Avenue on Wednesday night to round off the second round.
As Phillips referred to, Matlock have a home tie with York City in the third round.
Radcliffe will be at home to Spennymoor Town, who beat Chorley on penalties.
Lancaster’s prize is a trip to Morpeth Town, which means at least one NPL club will be in the fourth round.
Nantwich also face a long trip on the road, against King's Lynn Town.
If Marine can get past Bradford PA, they will host National League side FC Halifax Town, while Ashton United would have a trip to Chesterfield if they beat Guiseley.