The German side appeared to be heading for a comfortable finish after Guirassy's second goal made it 3–1, but an unfortunate own goal by the striker in stoppage time gave Villarreal renewed hope.
Dortmund nevertheless held on for three points in their opening league-phase fixture.
Karetsas Medical Scare Overshadows First Half
The biggest concern of the night came in the first half when 18-year-old Konstantinos Karetsas was forced off after experiencing circulation problems.
The Greece international, who had recently joined Dortmund, collapsed without an obvious challenge and required medical attention before being carried from the pitch on a stretcher.
Karetsas was subsequently taken to hospital for further examination. Reports citing Borussia Dortmund said the midfielder was in stable condition under the circumstances, although further medical assessment was required.
The incident understandably overshadowed much of the opening period, with Ethan Nwaneri coming on as Karetsas' replacement.
Villarreal Make Strong Start
Villarreal looked the more assured side during portions of the first half and created opportunities without finding the breakthrough.
The Spanish visitors threatened from set pieces and through their attacking players, but Dortmund's defence managed to keep the score level.
The hosts struggled to create clear-cut opportunities before the interval, with the loss of Karetsas adding to an already difficult evening for Niko Kovač's side.
The teams therefore went into half-time level at 0–0.
Renato Veiga Own Goal Gives Dortmund Lead
Dortmund emerged from the interval with greater attacking purpose and eventually broke the deadlock in the 53rd minute.
Villarreal defender Renato Veiga inadvertently turned the ball into his own net, handing Dortmund a 1–0 advantage.
The goal changed the momentum of the contest, with Dortmund beginning to attack with greater confidence.
Mouriño Brings Villarreal Level
Villarreal responded impressively.
The visitors equalised in the 66th minute, when Santiago Mouriño headed home from a corner to make it 1–1.
The goal gave Villarreal renewed belief and ensured the final stages would be fiercely contested.
Guirassy Takes Control
Dortmund regained the lead in the 80th minute.
Fabio Silva, introduced from the bench, made an immediate impact by helping create the opening for Guirassy, who finished from close range to put Dortmund 2–1 ahead.
The striker then had another opportunity to put the match beyond Villarreal.
Dortmund were awarded a penalty in the 85th minute after a tussle between Guirassy and Mouriño inside the box.
Guirassy stepped up and converted, sending the goalkeeper the wrong way to make it 3–1 and complete his brace.
Late Own Goal Creates Nervous Finish
Villarreal refused to give up.
In stoppage time, Guirassy inadvertently scored an own goal, reducing the deficit to 3–2 and setting up a tense finale.
The visitors pushed forward in search of an unlikely equaliser, but Dortmund managed to withstand the late pressure and secure the victory.
Dortmund Begin European Campaign With Three Points
The 3–2 victory gives Borussia Dortmund an important three points from their opening Champions League league-phase match.
It was also a significant result for Kovač's side, who had already started their domestic campaign strongly and now have consecutive competitive victories.
However, the celebrations were understandably tempered by the concern surrounding Karetsas.
Dortmund will hope the young midfielder's medical examinations provide positive news after what was an alarming moment at Signal Iduna Park.
The victory means Dortmund have started their European campaign on a winning note, but the health of Karetsas remains the most important concern following an eventful night in Germany.