WASHINGTON — Riding a powerful wave of voter discontent, resurgent Republicans captured control of the Senate and tightened their grip on the House Tuesday night in elections certain to complicate President Barack Obama’s final two years in office.

The Republican Senate leader, Mitch McConnell, dispatched Democratic challenger Alison Lundergan Grimes in Kentucky after a $78 million campaign of unrelieved negativity. Voters are “hungry for new leadership. They want a reason to be hopeful,” said the man in line to become majority leader and set the Senate agenda if his party gains control.

Two-term incumbent Mark Pryor of Arkansas was the first Democrat to fall, defeated by freshman Rep. Tom Cotton. Sen. Mark Udall of Colorado was next, defeated by Rep. Cory Gardner. Sen. Kay Hagan also lost, in North Carolina, to Thom Tilllis, the speaker of the state House.

Republicans also picked up seats in West Virginia, South Dakota and Montana, where Democrats retired. They needed a net gain of six seats in all to end a Democratic majority in place since 2006.

With dozens of House races uncalled, Republicans had picked up nine seats in Democratic hands, and given up only one.