Counting himself lucky to be playing professional sport for a living instead of working in the "real world", Allen fired a dazzling seven-under-par 63 on the hilly layout to break clear of a congested leaderboard with a 10-under total of 130.
Rocco Mediate, who lost a playoff to Tiger Woods for the 2008 US Open at Torrey Pines, was alone in second after carding a 67, with fellow American Jeff Sluman (also 67) a further stroke back at four under.
Only nine players in the field of 153 ended the round under par after 36 holes, among them overnight co-leader Kenny Perry who followed his opening 67 with a 73 to sit joint 10th, with Fred Couples (69) and Tom Watson (70) among others.
Allen, who clinched his first major title in his debut on the over-50s Champions Tour at the 2009 Senior PGA Championship, took control on a hot and breezy day at Omaha Country Club with his lowest score on the US circuit this year.
One of seven players tied for the lead after the opening round, Allen surged ahead with five birdies in the first eight holes to reach the turn in five-under 30.
Though he dropped his only shot of the day at the par-four 12th, he immediately responded with a birdie at the 13th before sinking a long-range eagle putt on the 14th green to maintain his stranglehold at the top of the leaderboard.
"It was one of those days I guess that's why you shoot 63, because a few things were really going right for me," Allen, 54, told ESPN.
Asked to explain his late golfing renaissance with four victories in the senior ranks after failing to win a single title on the US Tour where he competed in more than 350 events, Allen replied: "I'll make it short.
"When I quit playing after seven years on (the US PGA) Tour, you go back and try and work in the real world and you see how hard the real world really is.
"So it's that perspective that really changes things. I realise I really enjoy being out here. I am blessed to be able to do this and have an opportunity, especially at this age."
Allen's five-stroke lead after 36 holes is the largest in the event's 34-year history.
Englishman Roger Chapman, who won last year's US Senior Open by two strokes in Lake Orion, Michigan, was among those who missed the cut which fell at five-over 145.
"Just played rubbish," Chapman said after battling to a 76. "Drove the ball terrible. Had one birdie. That's it.
"I hit it okay on the practice ground, and just it's a mental block now. Just can't hit a fairway. If you can't hit a fairway out here, you can't score. Simple as that."
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