Gerrard kicks off Rangers career with a win
Jamie Murphy's low first-half finish and James Tavernier's injury-time penalty proved enough to give the 54-time Scottish champions a two-goal lead to take into next week's second leg of the first-round qualifying tie.
Former England captain Gerrard, whose only previous coaching experience came with Liverpool's youth teams, gave debuts to his former Liverpool team-mate Jon Flanagan and ex-Burnley midfielder Scott Arfield.
The hosts broke the deadlock in the 23rd minute, as Murphy, who only joined on a permanent deal from Premier League side Brighton in May, drove a low shot through Shkupi goalkeeper Suat Zendeli, who should have done better, to score the first goal of the Gerrard era.
The visitors had started brightly, with Blagoja Ljamcevski hitting the crossbar early on, but Rangers dominated after Murphy's strike, only for their profligacy to keep their opponents in the tie.
Colombian striker Alfredo Morelos got the ball caught under his feet when in space in the box, while Arfield miskicked with the goal at his mercy.
Rangers started slowly in the second period before the introduction of Liverpool loanee Ovie Ejaria livened things up, but Josh Windass headed over when unmarked.
The Scots boosted their hopes of avoiding a repeat of last year's humiliating exit at the same stage to Liechtenstein outfit Progres Niederkorn, though, as Murphy was brought down to win a 91st-minute penalty.
New captain Tavernier stepped up to slam the ball down the middle, cuing a fist-pump from the watching Gerrard.