The world and European champions' victory, to which Pedro contributed a 20th-minute goal, was their 39th in 44 matches under coach Vicente del Bosque, putting him one clear of his immediate predecessor Luis Aragones to set a national record.
Striker Villa gave the visitors the lead in the fifth minute when his curling shot from a central position 35 metres out beat goalkeeper Renny Vega low to his left.
It was his 47th goal in 75 internationals, extending his lead over Raul (44) at the top of the scoring chart.
After Pedro made it 2-0 with a deflected shot from Villa's assist, Alonso's strike moments before halftime found a gaping hole in the defensive wall and Vega couldn't get down in time to save, this time to his right.
Venezuela showed plenty of industry but were outclassed by the slick Spanish, who left several first-choice players, including captain and keeper Iker Casillas, out of their starting line-up.
The home side's best chance fell to Giancarlo Maldonado in the 18th minute when he sped clear into the penalty area but his low shot was saved by the onrushing Victor Valdes.
Cameroon held Russia to a 0-0 draw and almost won with a late header that hit the post in a friendly in the Alpine city of Salzburg.
Cameroon's Aurelien Chedjou's struck the woodwork towards the end of a largely uneventful match which was interrupted with two minutes remaining when several fans ran onto the pitch.
The Indomitable Lions were licking their wounds after a goalless draw against visiting Senegal on Saturday left their African Nations Cup qualifying hopes hanging by a thread.
Russia, meanwhile, had enjoyed a 3-1 win over Armenia in a Euro 2012 qualifier at the weekend that kept them level on points with the leaders in their group.
Russia's Dutch coach Dick Advocaat made wholesale changes from Saturday's match, giving several players their debuts, and his side looked livelier in a first half played in pouring rain.
Russia striker Pavel Pogrebnyak sent a low close-range shot wide early on and Alan Dzagoyev also missed the target from the edge of the box midway through the half.
But the African team came alive towards the end of the game, creating several chances of their own.
Pierre Webo, who replaced captain Samuel Eto'o at halftime, saw his powerful header tipped over by Russia's second-choice goalkeeper Vyacheslav Malafeyev while Chedjou's header hit the post less than a minute later.
"We had a few chances and should have won this game," Advocaat said. "But I have to be satisfied with our effort."
There had been some light relief when one of the intruders who ran on to the pitch kicked a ball in the Cameroon goal to the amusement of the players, fans and Austrian referee Thomas Einwaller before they left the arena with no security in sight.
It was the first game between the two countries since Russia thrashed Cameroon 6-1 in the 1994 World Cup when striker Oleg Salenko set a record with five goals in a match at the finals.
Cameroon have had a turbulent week with fans rioting after Saturday's home draw with Senegal in which Eto'o missed an 87th minute penalty all but dashing their hopes of qualifying.
Australia and Serbia also played out a goalless stalemate, as did Japan and the Czech Republic - ending a run of 13 consecutive matches in which the Japanese scored at least one goal.
Austria enjoyed a relative goalfest thaks to three late goals as they recovered from a goal down with 20 minutes to go to beat Latvia 3-1 in Graz. Martin Harnik scored twice for the home side.
In Belgium, the Republic of Ireland recorded a memorable 2-0 win over Italy (see separate report).