Ouseph, 30, who won European gold in April, beat Mendrek 21-15 21-13 in the men's singles in Glasgow.
"I feel like I'm in career-best form right now," Ouseph told BBC Sport.
Scotland's Kieran Merrilees lost to two-time Chinese Olympic gold medallist Lin Dan and Sarah Walker and Lauren Smith of England beat Germany's Lisa Kaminski and Hannah Pohl.
The European bronze medallists and world number 27 pairing won in straight sets (21-10 26-24) to reach the round of 32.
"We showed a lot of character and we're really happy with how we performed," Walker told BBC Sport.
Smith added: "We got stuck in and it was an awesome experience today."
Merrilees said he struggled with nerves in the build-up to and throughout his encounter with Lin, who won Olympic gold at Beijing 2008 and London 2012 and is targeting a sixth world title.
"I've been dreading it since I learned of the draw to be honest," Merrilees told BBC Sport.
"I thought I was going to be sick pretty much from the beginning - and I let it get to me which is really frustrating."
England's Ben Lane and Jess Pugh fought back after losing the opening set 14-21 to Dutch pair Robin Tabeling and Cheryl Seinen to take the next two 21-16 21-14.
English Commonwealth champions Chris and Gabby Adcock will start their bid to become Britain's first world badminton champions since 2006 on Tuesday.
Rio Olympic bronze medallists Chris Langridge and Marcus Ellis, as well as Scotland's European silver medallist Kirsty Gilmour, have received opening-round byes and will begin their events on Wednesday.
England's Rajiv Ouseph eased into the second round of the World Championships by beating Czech player Adam Mendrek.