Forward Alcacer, who scored on his competitive Spain debut in this month's 5-1 Euro 2016 qualification victory against Macedonia, fired Valencia ahead in the seventh minute at Getafe's Coliseum stadium in the Madrid suburbs.
Midfielder Andre Gomes made it 2-0 in the 20th minute.
Striker Rodrigo had an eventful second half when he netted a 72nd-minute penalty before earning a second yellow card and getting sent off a minute later.
The victory lifted Valencia into second place after four matches, level on 10 points with Sevilla and two behind early leaders Barcelona, the only team with a perfect record.
Four-times World Player of the Year Lionel Messi starred as Barca scored a thumping 5-0 win at Levante on Sunday, while champions Atletico Madrid have eight points in fourth following Saturday's 2-2 draw at home to Celta Vigo.
Real Madrid are seventh on six points after they hammered hapless Deportivo La Coruna 8-2 on Saturday to help the stuttering European champions put consecutive La Liga defeats behind them.
Hopes are high at Valencia, who failed to qualify for Europe last season, that a takeover by Singapore billionaire Peter Lim will help the club put years of financial woes behind them and transform them into genuine challengers in domestic and continental competition.
Lim's purchase of the club is close to completion, although reports in Spain have said talks with Valencia's main creditor Bankia have broken down.
(Reporting by Iain Rogers, editing by Alan Baldwin)
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