The experienced Allenby, short of runs so far this season, made 64, his highest score since moving from Glamorgan in the winter. His efforts laid the foundation for Overton to replace him at the crease and plunder 55 runs from only 31 balls as Somerset collected three batting points.
Nottinghamshire replied with 57 for two from the closing 24 overs of the day.
Vernon Philander enjoyed his best day with the ball for the home side, returning figures of four for 56, against the side that he made a handful of appearances for in 2012.
The South African pace bowler seemed to relish the opportunity of playing against former team-mates, under cloudy skies, after Chris Read had won the toss and asked the visitors to bat first.
Marcus Trescothick has seldom enjoyed his previous visits to this famous old ground, having failed to register a century in 20 first class matches. His 33rd innings on the ground was typically brief, castled for nought by a wonderful swinging delivery from Philander.
Somerset also lost Tom Abell during the early exchanges but approached lunch in better order before losing three wickets to the final eleven balls of the opening session.
Two of those wickets were taken by Steven Mullaney, including Johannes Myburgh for 49, as the bowler enhanced his reputation as a partnership breaker.
That reputation, real or imaginary, prompted Read to turn to him again in mid-afternoon and again the all-rounder delivered, bowling Peter Trego to end a stand of 85 in only 15 overs, made alongside Allenby.
Craig Overton made the most of some wayward bowling to plunder 10 boundaries in a quickfire 50 before being cleaned up by Harry Gurney.
Seven of the ten Somerset dismissals came via the ‘bowled’ method of dismissal after Luke Wood collected two late scalps.
The 19 year old left arm quick dumped Lewis Gregory on his backside with a well-directed bouncer before bowling him next ball, then wrapped up the innings by yorking Tim Groenewald.
When Nottinghamshire batted they lost the wickets of Mullaney, to Gregory for 19, and Greg Smith for 8.
Smith, on his county debut, failed to make the most of his opportunity to step in for the absent Alex Hales by falling lbw to Groenewald for 8.
Hales’ weekend dash to India to join the Mumbai Indians in the Indian Premier League had gone unrewarded when he was left out of their final qualifying match against Sunrisers Hyderabad.