Evans recovered from a set down to defeat Brazilian qualifier Thiago Monteiro 6-7 6-2 7-6 and will play Mischa Zverev, the German 14th seed who knocked Andy Murray out of the Australian Open in January, in the second round.
Edmund sailed through in straight sets 6-3 6-4 against world number 70 Jeremy Chardy and will face fourth seed Dominic Thiem of Austria.
Local favourite Tommy Robredo lost 6-4 6-3 to Yuichi Sugita of Japan. However, there was better news for the home crowd as Nicolas Almagro beat Canada's Steven Diez 6-3 6-4.
The line-up for the second round will be confirmed on Tuesday, with Dustin Brown versus Bernard Tomic the pick of the day's action. The winner will face Murray.
Read the original article on Eurosport: Edmund and Evans through but home favourite Robredo loses