The opening half was a closely contested affair, with both sides enjoying promising opportunities. Facundo Alvarez and Nico Pinto both went close for the Imps, while Jaylan Hankins was called into action on several occasions to keep the Cypriot side at bay as the teams went into the interval level.
The second half followed a similar pattern, with chances at a premium until the breakthrough finally arrived in the 71st minute. Alvarez delivered an inviting corner into the penalty area, where Christian Rutjens rose highest to power a header beyond Fabiano Freitas and send the Europa Point crowd into celebration.
Looking to preserve the advantage, Juanma Pavón introduced fresh legs with Alex Mula, Ethan Jolley, Leon Mason - making his club debut - and Ethan Britto all entering the action as Lincoln absorbed increasing pressure from Omonoia.
However, heartbreak arrived in stoppage time. The visitors were awarded a free-kick on the edge of the final third, and after the delivery into the area, Hankins produced an outstanding double save to deny the initial efforts. Unfortunately, the loose ball fell kindly for Panagiotis Andreou, who converted the rebound in the 93rd minute to level the scores.
The 1-1 draw leaves everything to play for heading into next Thursday's second leg at the GSP Stadium in Nicosia, where a place in the UEFA Europa League play-off round against Belgian side Sint-Truiden awaits the winners.