Shaun Bammant's second half goal extended Lowestoft's unbeaten run to five games as well as giving them an FA Cup victory which have been all so rare in recent seasons.
Lowestoft were the first to threaten with Connor Deeks chipping the ball over the Ware defence to Andrew Fisk who lobbed the keeper but saw the ball drop agonisingly wide of the upright.
A partially cleared corner saw the ball fall to Adam Smith whose 25-yard screamer was turned round the post by the diving Harry Ricketts.
After weathering that early Lowestoft pressure, Ware started to come more into the game with the pacy Ben Hart causing the Trawlerboys defence many problems.
Firstly he sent a tantalising cross flashing across Elvijs Putnins' goal with Albert Adu just unable to get a touch and then trying his own luck grazing the post from 20 yards.
For the first 20 minutes of the second half, Lowestoft struggled to contain the home forwards. Dave Cowley saw his shot blocked by Rossi Jarvis but from the rebound in front of an open goal he blazed high over the top.
Ware were forcing a number of corners and from one of them Putnins failed to cut it out leaving Jordan Watson with a free header which he sent over the bar.
The dangerous Hart put in another excellent cross but Cowley sent his header straight at Putnins. Lowestoft finally started getting back into the game and thought they had taken the leaf in the 66th minute when Fisk steered his shot from the edge of the area just inside the post but the goal was ruled out for an offside decision against Bammant.
Just three minutes later Bammant made amends sweeping in a Josh Curry cross to score what proved to be the winning goal.
Kieran Higgs hit the bar from the edge of the area but the final minutes saw the Lowestoft goal lead a charmed life thanks to some erratic finishing by the Ware forwards.
In the third minute of added time Curry was sent off for a second yellow card.
It was probably the Trawlerboys' poorest display of the season but earned them a place in the second qualifying round draw.
Ware: Ricketts, Madden (Yexley 82), Baird, Brown, Rose, Frasier, Hart (Diakiesse 88), Cowley, Rose, Adu (Haag 82), Watson. Subs not used: Gkontsarov, Appiah, Hannam, Long.
Lowestoft Town: Putnins, Curry, Deeks, Smith, Jarvis, Fisk (Pinheiro 90), Schaar, Higgs, Bammant, Fowkes (Brown 66), Zielonka (Pollock 80), Subs not used: Tann, Reynolds.
Referee: Mr T Donnellan
Attendance: 173
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here