Having been put in to bat, the visitors slipped to 101-5 but their lower middle-order and tail managed to lift the total to 312 and they then reduced Nottinghamshire to 57-2 at stumps.
The hosts enjoyed a fine morning, the impressive Vernon Philander (4-56) bowling Marcus Trescothick for a six-ball duck with a beautiful swinging delivery and then having Tom Abell caught behind by Chris Read for 10.
Johann Myburgh (49) and James Hildreth (32) put on 78 for the third wicket but Steven Mullaney (3-44) then bowled Myburgh and had Tom Cooper (one) caught by James Taylor, Philander bowling Hildreth in between, as three wickets fell for just two runs.
But Allenby and Peter Trego (41) began the recovery with a stand of 88 for the sixth wicket which Mullaney ended by bowling Trego.
Lewis Gegory was then dismissed by Luke Wood after contributing 17 and it was 241-8 when Philander ended Allenby???s good knock.
But Overton then produced some real fireworks, smashing 11 boundaries in his 31-ball knock and adding 70 for the ninth wicket with Alex Barrow (23 not) in just over eight overs until he was bowled by Harry Gurney.
When Nottinghamshire replied, Mullaney and Brendan Taylor put on 36 but the former was then trapped in front by Gregory for 19.
Greg Smith (8) was making his debut for the county but also went lbw, in his case to Tim Groenewald, but Brendan Taylor (11 not out off 73 balls) and James Taylor (3 not out) survived for just under half an hour to reach stumps.
Allenby said: “Having got 300-odd, we felt that was over par, especially after we’d??had a bit of a wobble in our last few games. It was nice to get it right??today in difficult conditions.”
There was also a cracking day???s play at Edgbaston, where Warwickshire rattled up 417-7 against Durham, having been 18-2 and 227-6 at various points.
Jonathan Trott began life in international retirement with 42 but was overshadowed by the dogged Ian Westwood (88) and the attacking eighth-wicket pair Keith Barker and Jeetan Patel
For Durham, seamer Graham Onions (4-74) advanced his case for an England recall, taking four key wickets.
The hosts opted to bat first but skipper Varun Chopra (13) was caught behind by Phil Mustard off Onions and Chris Rushworth trapped William Porterfield (one) lbw.
That made it 18-2 but Westwood and Trott lifted Warwickshire to 102 before Trott (42) fell lbw to the second ball after lunch from Onions, having looked in assured form.
Laurie Evans (45) and Westwood then put together another good stand, adding 106 for the fourth wicket before Onions struck again, having Evans caught behind and then bowling Westwood with a lovely delivery which clipped off stump.
When Tim Ambrose became Mustard???s 641st first-class victim, caught behind off John Hastings for 13, Warwickshire were wobbling on 227 for six, but Rikki Clarke (36) and Barker put together a swashbuckling stand of 103 ??in 14 overs.
And the fun continued for the hosts after Clarke???s departure, Barker (86 not out off 101 balls) and Patel (50 not out off 46 balls) pummelling the bowling, as they put together an unbroken stand of 87 in 15 overs prior to stumps.
Hampshire made an encouraging start to their match with leaders??Middlesex at the Ageas Bowl, closing on 295-5 after being put in under overcast skies.
Jimmy Adams and Liam Dawson (36) did well to see off the new ball and took their partnership to 85 before Dawson was caught behind by John Simpson off Neil Dexter.
Left-handers Carberry and skipper Adams then added 75 for the second wicket, before the country???s leading wicket-taker James Harris broke the partnership by bowling Adams with a beautiful yorker, the Hampshire captain falling for a patient 61.
That brought James Vince to the crease and he helped Carberry add 49, only to hole out to Dexter at deep mid-on off Ollie Rayner for 27 not long before tea, which Hampshire took at 211-3.
Carberry was looking in fine nick and he reached 67 before he was caught by James Franklin off Harris and Steven Finn trapped Adam Wheater (7) lbw with one which may have kept a little low.
However, Will Smith is not out overnight, having made it back-to-back Championship fifties when he moved to 52 not out off the final ball of the day.
Hampshire coach Dale Benkenstein said: “When you are put in it is always good to come in after scoring 300, you know you have had a good day.
“It was very tricky conditions. Daws only got 30 odd but there are good 30s and bad 30s and that was a good one – I though he batted unbelievably well.
“The platform him and Jimmy set helps the rest of the order. Every run in this first innings is like gold in these conditions.”