The veteran Ottawa defenceman gave his team a 2-1 lead on a power play at 4:36 of the period with a long shot that eluded goalie J.S. Giguere.
The Anaheim goaltender had lost his stick about 20 seconds before and was still struggling to grab it when Redden's shot beat him.
Anaheim held a physical advantage in the game but it was having trouble keeping that in control. Through two periods, the Ducks had taken seven penalties while Ottawa had been assessed just two.
Both of Ottawa's goals in the opening 40 minutes of Monday's game came with a man advantage, but the Senators were unable to capitalize on 5-on-3 shortly after Redden had made it 2-1.
Mike Fisher and Andy McDonald exchanged first-period goals.
The Senators got on the board just 1:38 into the game. With Ducks captain Scott Niedermayer in the penalty box for high-sticking, Fisher took a shot that bounced off Giguere's glove and went high into the air before trickling over the goal-line.
The goal was originally awarded to Senators forward Mike Comrie, but was later changed to Fisher. It hardly mattered to Ottawa, which was 8-0 in the first three playoff rounds when scoring first.
The Ducks soon battled back to the delight of an enthusiastic sellout crowd at Honda Center. The Anaheim forwards were hitting everything in sight and creating pressure in the offensive zone.
McDonald's sixth goal of the playoffs at 10:55 evened the score at 1-1.
Rookie Andrew Miller, the brother of Buffalo Sabres goalie Ryan Miller who was playing just his second NHL game, hit Ottawa defenceman Wade Redden to cause a turnover. Teemu Selanne picked up the puck and found McDonald, who beat Ray Emery with a quick shot.
Anaheim continued to press with a good shift from its energy line, but Emery kept them from taking the lead.
The teams haven't played each other in over a year, but bodies were flying everywhere during a physical opening two periods in Game 1.
Ottawa and Anaheim were ready to go despite the long layoff before this series.