The battle of the unseeded players - both ranked inside the world's top 55 - was an armchair ride for the Spaniard.
"I was more consistent and I served well," said Vicente.
Winning four of eight break points - and without handing any to Squillari - Vicente cruised into the second round, where he will play either fifth seed, and former open winner, Czech Jiri Novak or Italian Andrea Gaudenzi who meet first up this morning on an outside court.
Such is the calibre of today's matches, three previous winners - Novak, Jonas Bjorkman, Sjeng Schalken - play their first round matches away from centre court.
Of earlier winners here, only defending champion Dominik Hrbaty of Slovakia will grace centre court today but even he has been relegated to playing first up (at 11 am).
Hrbaty, the tournament's eighth seed, meets Belgian qualifier Gilles Elseneer in the curtainraiser to the big day out, with top seed Russian Marat Safin and wildcard Michael Chang next on.
Second seed Goran Ivanisevic meets world No 61, Finn Jarkko Nieminen, in game three.
In the last match of the day session, last year's beaten finalist and the oldest player in the tournament, 33-year-old Spaniard Francisco Clavet plays American third seed Jan-Michael Gambill.
Though the day session has long been a sellout, there might be some tickets left for tonight's action which features big-serving sixth seed Briton Greg Rusedski, and regular visitor Argentine Mariano Zabaleta.
To cap off "terrific Tuesday" New Zealand singles hero Mark Nielsen teams with US-based James Shortall in the doubles against Australian Andrew Kratzmann and Swede Simon Aspelin.
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