The visitors made it 2-1 at Seaview when Bennett scored at the correct end, nodding in a corner at the near post in the 38th minute.
Jimenez fired in his second on the stroke of half-time, before a Jordan Forsythe own goal deep into the second half (77’) sealed a routine victory for the Premier League outfit.
Nuno Espirito Santo’s men now face a gruelling 6,370-mile round trip to face Armenian club Pyunik on August 8, just three days before kicking off the Premier League opener against Leicester City.
RANGERS ALSO THROUGH
Meanwhile, Rangers sealed their place in the third qualifying round after playing out a goalless draw against Luxembourgian side Progres Niederkorn which followed a comfortable 2-0 win in Glasgow last Thursday.
Rangers’ best effort fell to Scott Arfield in the opening stages as he rounded the goalkeeper, but he failed to convert. Nevertheless, Steven Gerrard’s side eased through and will travel to the MCH Arena in Denmark to take on Midtjylland for their first leg on August 8.