Republican Sen. Thad Cochran's runoff victory Tuesday exposed the limits of tea-party power at the polls, but conservative activists retain considerable influence in Congress as they fight the Export-Import Bank, an immigration law overhaul and higher taxes to repair bridges and roads.

Mr. Cochran's narrow win over a tea-party-backed challenger, coming after the defeat of conservative activists in other primary elections this year, offered further proof that GOP leaders and their business allies have built a successful strategy...