AFC Emley bowed out of the FA Carlsberg Vase after a valiant first round effort.
Andy Fowler was on target for hosts Bootle with two second-half strikes.
In the first half both defences dominated the tie with scoring chances few and far between.
But Nicky Bramald and Ray Dennis’s team stepped up a gear in the second half and had a real go against the Merseysiders who are ninth in Division II of the North West Counties League.
On 50 minutes skipper Sean Hazelden pushed up from his central defensive position and was unlucky to see his towering header cleared off the line. But almost immediately afterwards Bootle, who were proving dangerous on the break, counter-attacked upfield and Bootle’s man-of-the-match Fowler fired his side into a 1-0 lead.
Northern Counties East League Division I side Emley continued to press but, once again, were caught on the counter-attack when Fowler added a second on 83 minutes to seal a place in the second round, where they will host Winterton Rangers, who are second in the NCEL Premier Division on Saturday, November 17.
AFC Emley, 11th in Division I, host basement club Rossington Main at the Welfare Ground on Saturday (3.00).
Elsewhere, there were mixed fortunes for minor league clubs in the second round of the West Riding FA Sunday Cup.
From six Huddersfield Sunday League teams still in the competition, only three progressed to the third round. Division I leaders Heywood Irish Centre started slowly away at Littletown (Sunday) but found their scoring touch to take a 2-0 lead at the break.
The second half was one-way traffic as Irish added a further four to win convincingly 6-0 thanks to a John Paul Flynn hat trick plus others scored by Ashley Flynn, Matt Tattersley and Darren Henighan.
Walpole Community travelled to Bradford to face Nabwood JFC and edged a close 2-1 victory with Richard Lewis and Lloyd James on target.
Heywood Irish Centre moved top of the Huddersfield District League after Mowforth scored the only goal of the game in their 1-0 victory against New Mill 94.
The result gives Heywood a one-point lead at the top from Uppermill.