Watson, who won the Senior British Open and The Tradition last year, posted a 4-under-par 67. He was joined there by Irwin, the Champions Tour all-time wins leader.
The first round was delayed by two hours at the outset due to overnight rain. Over 3 inches of rain has fallen on the course in recent days with more forecast throughout the weekend.
On Thursday, action was called for the day at 7:41 p.m. ET due to lightning. The first round will resume at 8:30 a.m. Friday with the second round commencing at 9:45.
Gil Morgan stands in third place at 3 under par through 15 holes. Mike McCullough completed his round at 2-under-par 69. He shares fourth place at minus-2 with Craig Stadler, Jay Haas and D.A. Weibring, who have completed 15 holes as well as Bob Ralston (11) and Pete Oakley (10).
'On the first nine, I hit some pretty good quality shots and then on the back nine I got into a pretty good groove,' said Watson. 'I hit some very good shots on the back side. So that combined with a couple good putts, the last three holes, it was a good round of golf. My confidence is a lot higher now than it was yesterday.'
Watson began his day on the 10th tee at Valhalla Golf Club. He got up-and-down from in front of the par-5 10th for birdie. He then ran off seven straight pars. Watson two-putted for birdie from the fringe on the par-5 18th to move to minus-2 heading to the front side.
The 2001 Senior PGA Championship winner missed the green at the par-4 second. Watson putted the ball through a chipping area, but left that shot well short. His par-saving putt rolled 6 feet passed the cup but he tapped that in for bogey.
Watson dropped a pitching-wedge within 10 feet of the cup at the sixth and sank that birdie try to get back to minus-2. He came back with a two-putt birdie at the next.
Watson, who shared 17th place at this event last year, knocked a 6-iron on the green at the ninth, his last. He sank the 18-foot birdie putt to get to 4 under and a share of first.
Irwin was unable to get up-and-down for par at the first. He reeled off four straight pars before dropping a 6-iron within 15 feet of the cup at the sixth. He sank that birdie putt to move back to even par.
After three more pars, Irwin stuck his third shot to the par-5 10th within 2 feet for birdie. The 39-time winner on the Champions Tour rolled home at 25-foot birdie putt at the 15th to get to minus-2.
Irwin sank a 6-footer for birdie at the 17th to get within one shot of Watson. He then two-putted from 30 feet for birdie at the last to share the lead.
'Well, obviously I'm delighted to be in the position I am,' Irwin said. 'I did not start particularly well, but I did have a very, very solid back nine. The golf course was a little different than what we have seen in the last few days. As far as my play goes, pretty solid. I think I missed only one fairway today. All in all, I can't complain with the score I had.'
Tom Strueber, Doug Tewell, Bobby Walzel and Mark McNulty each carded rounds of 1-under-par 70. They share 12th place with Gavin Levenson, Wayne Levi, Dave Barr, Will Frantz, John Harris and Mike Smith, who all have to complete their first rounds.
John Jacobs, the defending champion, posted a 3-over-par 74 where he shares 58th place