Janowicz is to face Joao Sousa in the last 16 after the Portuguese beat Guillermo Garcia Lopez 6-3, 7-5.
No. 3 seed Almagro stayed on course for a potential semi-final meeting with Janowicz or David Ferrer with a 6-2, 6-3 success over compatriot Pablo Andujar.
Almagro was completely dominant in the first set and despite losing his own serve for the only time in the match early in the second, he broke Andujar three times to close out a comfortable victory.
There was more disappointment for Australian Bernard Tomic as his frustrating year continued when he was forced to retire in the third set against Mikhail Youhzny, with the Russian leading 3-6, 6-4, 4-1.
It was not a good day for home favorites Fernando Verdasco and Feliciano Lopez, as they fell in straight sets to Michal Przysiezny and Julien Benneteau respectively.
Top seeds Ferrer and Tommy Haas begin their campaigns in the coastal Spanish city yesterday.
Ferrer faced an extremely tough first-round tie with Gael Monfils as he aims for a fourth title in Valencia, whilst Haas was to face compatriot Philipp Kohlschreiber as he continues his quest to make it to the ATP World Tour Finals in London next month.