The Oundle School fly half's three-pointer rewarded a long spell of pressure and nudged England back in front in a game that saw momentum swing from one team to the other.
Olver kicked an earlier penalty, which when added to a pair of tries saw England go out to a 13-0 lead. But Ireland fought back to go 15-13 up as the clock ticked down until Olver's late intervention.
"To be honest we should have been out of sight by half time," said head coach John Fletcher. "We scored two tries but it should have been more - we left a few out there.
"In the second half Ireland came back fighting and we seemed to lose some of our composure, two guys went into the sin-bin [Gus Jones and Danny Hobbs-Awoyemi] and we were staring a defeat in the face at 15-13 down.
"Full credit to guys for battling back and putting Sam in a position to get his drop goal. Overall it's been a good experience, a good exercise, and a good test for our players."
Centre Tom Stephenson and prop Danny Hobbs-Awoyemi also started the game, the latest England age group success to feature several members of the Saints Academy.
Half-a-dozen players, including Stephenson and Hobbs-Awoyemi, helped England Under-20 to the 2013 Six Nations title in March, while a quartet of Under-18s starred as England retained the FIRA/AER Championship last weekend.
ENGLAND UNDER-19 TEAM TO PLAY IRELAND
Wednesday, March 3rd, 2013
Kick off 1:00pm
15 Nathan Earle (Saracens)
14 Zach Kibirige (Newcastle Falcons)
13 Tom Stephenson (Northampton Saints)
12 Javiah Pohe (Leicester Tigers)
11 Josh Watkins (Worcester Warriors)
10 Sam Olver (Northampton Saints)
9 Jordan Burns (Harlequins)
1 Danny Hobbs-Awoyemi (Northampton Saints)
2 Harry Thacker (Leicester Tigers)
3 Adam Jamieson (Bath)
4 Maro Itoje (Saracens)
5 Tom Ellis (Bath)
6 Ross Moriarty (Gloucester)
7 Gus Jones (London Wasps)
8 Hayden Stringer (Saracens)
16 Cameron Neild (Sale Sharks)
17 Alex Lundberg (London Wasps)
18 Jake Armstrong (Leeds Carnegie)
19 David Hughes (London Wasps)
20 Lewis Ludlow (Gloucester)
21 George Tresidder (Leicester Tigers)
22 David Buck (Bath)
23 Tom Hudson (Leicester Tigers)