Morgan, who held the outright lead entering round three, posted a 70 and shares the lead at the season's fifth and final major with Tewell at 13-under- par 203.
Mark McNulty and Tour rookie Loren Roberts are one stroke further back at minus-10.
Tewell, the 2001 champion of this event, started his round with four straight pars. He then rolled in a birdie putt on the fifth and made it two straight with a birdie on six on the South Course at The Reserve Vineyards & Golf Club.
The eight-time winner on the Champions Tour parred seven and eight, before he drained his third birdie on the ninth to turn at minus-10. After parring the first two holes of his second nine, Tewell birdied the par-4 12th.
Tewell ran home back-to-back birdies from the 15th to move to 13 under and closed with consecutive pars to finish there.
'Sunday is going to be a lot of fun,' said Tewell. 'I know they are laughing back at home, because Gil and I never play much golf at home. So this is an opportunity for he and I to play together. He and I go out and chip and putt a lot late in the day.
The only time Tewell held the lead after three rounds was back in 2001 when he won this title. Tewell went on to fire a 62 in the final round to win by nine strokes.
'It's going to be a lot of fun,' Tewell said. 'I think the key is for both of us to play the course and not each other.'
Morgan, a two-time winner of the Tradition, was steady throughout his round, as he battled to 15 consecutive pars to start his day.
The 58-year-old finally got on the board with a birdie on the par-5 16th. Morgan, who holds a Doctor of Optometry degree but has never practiced, then parred the 17th before sinking a birdie putt at the last to share the third-round lead.
'That was the main thing. I knew if I could do that, I was definitely assured of playing with Doug,' said Morgan, who practices often with Tewell.
Morgan does have his work cut out for himself if history holds. In the season's first four majors, not one of the 36-holes leaders has gone on to win the title. He has won three of the five times he has led on the Champions Tour after three rounds, including his title at this tournament in 1997.
Mark James, Mark McCumber, Jerry Pate and D.A. Weibring are tied for seventh at 9-under-par 207. John Harris and James Mason are two strokes further back at minus-seven.
Of the four majors champions from earlier in the season, U.S. Senior Open champion Allen Doyle is closest to the leaders. He posted a 1-under 71 and stands in a tie for 14th at 4-under-par 212.