Roberts struggled to a 5-over 75 in the final round to end at 6-under-par 274. Romero managed a 1-over 71 to join Roberts in the playoff at the Ailsa Course at Westin Turnberry Resort.
Romero knocked his second shot to the back of the green, then watched Roberts drop his third shot within 20 feet. Romero's birdie effort stopped 6 feet from the cup.
Roberts poured in his par putt, then Romero missed his 6-footer, giving Roberts the crown. This was Roberts fifth Champions Tour win -- fourth this year -- and second major title on the senior circuit after the 2005 JELD-WEN Tradition.
Dick Mast carded the low round of the day with his 3-under 67, moving him to 5-under-par 275 for third place. He was one of four players to shoot in red figures in the final round.
Former Masters champion Craig Stadler shot an even-par 70 to take fourth place at 2-under-par 278. Tim Simpson was one stroke further back at minus-1 after a 4-over 74 on Sunday.
Roberts and Romero dueled throughout the round. Roberts was in command at the outset, but Romero caught him on the 10th and that was when things really got interesting.
The 51-year-old Roberts opened with back-to-back pars and led by five as Romero bogeyed the second. Roberts tripped to a bogey on No. 3 and another at the fifth.
Romero birdied No. 5 to close within two of Roberts. The 52-year-old Romero moved within one thanks to a birdie at the seventh.
Both players birdied the ninth, then Romero joined Roberts at minus-10 with a birdie on No. 10. Roberts regained the top spot with a birdie on 11.
Roberts bogeyed the 12th, then stumbled to a double bogey at 14 to drop to minus-8. He still led by one, though, as Romero bogeyed 12, 13 and 14 to slide to 7 under par.
At the 16th, Romero gave another stroke back with a bogey that left him at minus-6. However, Roberts double bogeyed the same hole to fall into a tie for the lead. They each parred the final two holes to head to the playoff.
The struggles down the stretch for Roberts were reminiscent of the Senior Players Championship where he led by two entering Sunday and by as many as five strokes during that final round. Roberts stumbled to a 2-over 74 and eventually finished two shots behind winner Bobby Wadkins.
Senior PGA champion Jay Haas and D.A. Weibring each posted rounds of 2-under 68 Sunday to end in a tie for sixth place at 1-over-par 281. Gil Morgan and David Edwards were two strokes further back at plus-3.