The Eagles grabbed their chances to take a shock lead, but once Betts had doubled his tally for the season with his first two tries Wigan were always in charge and his third near the end merely underlined their superiority.
Sheffield had to defend superbly against insistent Wigan pressure for virtually all the first quarter but still managed to score on their first two attacks. They had already soaked up plenty of punishment when crisp handling from Johnny Lawless, Steve Malloy and Rod Doyle sent Simon Baldwin over.
The Eagles were pounded again straight from the kick-off, but held firm once more to hit Wigan on the counter-attack. The inspired Doyle handled twice in the move, sending Darren Turner through with a short pass and then releasing Matt Crowther to show his old, pre-knee operation pace to score.
With two conversions from Martin Pearson, the Eagles had a handy lead, which could have been even better if a spell when they forced Wigan to drop out from under their posts into a strong wind on three occasions had yielded another score.
Instead, Wigan regained possession with the calculated gamble of a short kick and drove downfield for Mick Cassidy to send Betts over for his first.
Five minutes from half-time, Sheffield conceded possession in strange fashion, Pearson's attempt at a clearing kick being blocked by a team- mate to give Wigan the ball from a scrum. This time Betts surged over from dummy half and Andy Farrell's second goal put the reigning champions level at the break.
Four minutes into the second half, Farrell dummied his way over and added his third goal as Wigan took the lead for the first time. Betts completed his hat- trick 11 minutes from time, holding off Chris Thorman's ineffectual attempts to tackle him as he charged down the right touchline and Farrell's clever kick then set up Kris Radlinksi. The Wigan captain finished with six goals from six attempts.
Sheffield Eagles: Watson; Sodje, Cardoza, Senior, Crowther; Pearson, Stephens; Molloy, Lawless, Baldwin, Turner, Shaw, Doyle. Substitutes used: Thorman, Hardy, Molyneux, Sovatabua.
Wigan Warriors: Radlinski; Robinson, Moore, Connolly, Johnson; Florimo, T Smith; Cowie, M Smith, Mestrov, Betts, Cassidy, Farrell. Substitutes used: Chester, Clinch, Gilmour, Goldspink.
Referee: S Presley (Castleford).