The Spanish club's close-season has been fraught with off-the-field insecurities regarding the club's financial status and ownership, but Sunday's match came hard on the heels of the news that businessman Lim has now cleared one of the last remaining hurdles required to take over the club after reportedly reaching an agreement with Spanish bank Bankia.
The Singaporean's impending purchase seems to have inspired Valencia supporters once again, with the Mestalla packed for the visit of the Serie A side.
Under new coach Nuno Espirito Santo, Valencia looked timid in the opening stages as Milan dictated possession, but the hosts took a spectacular 18th-minute lead after settling into the game.
New signings Rodrigo, Nicolas Otamendi and Andre Gomes all started, but it was Paco Alcacer, a rising star under the previous regime, who broke the deadlock when he pounced on Cristian Zapata's poor square pass before lobbing debutant Diego Lopez from fully 40 yards.
Keisuke Honda drew Milan level 10 minutes later as his 30-yard free-kick flew in via the right-hand post, but the Liga side restored their lead seven minutes before the break when Rodrigo squeezed between a couple of defenders and fired into the bottom-right corner.
The second period lacked the same intensity and flow of the first half, with a host of substitutions from both sides the likely cause.
The game did begin to liven up once more in the final 25 minutes, but neither side could add to the scoring.
Valencia substitute Sofiane Feghouli - on for Alcacer - went close when he skewed a shot wide from 12 yards in the 68th minute, before, at the other end, Jeremy Menez narrowly missed the corner with a shot from the edge of the area.
The best chance of the second half fell to Michael Essien with 12 minutes left, but replacement goalkeeper Yoel turned his header away in acrobatic fashion as Valencia held on to a morale-boosting victory just six days before they start their La Liga campaign at Sevilla.
