The Somerset opener has endured a lean start to the international season, making 16 and 15 in England's win at Lord's last week, and was dismissed by Tim Southee for just one this morning.
England, who named an unchanged side, won the toss and chose to bat first, reaching 32 for one after an hour's play.
Captain Alastair Cook was 12 not out, with Jonathan Trott looking in good touch on 17no.
Cook got the scoreboard moving by flicking the third ball of the morning to the fine-leg boundary and Compton was off the mark with a single into the on-side.
It was Compton's only scoring shot. He fell to the final ball of Southee's second over, playing away from his body and sending a smart catch to an alert Dean Brownlie at third slip.
Compton banked plenty of credit for back-to-back hundreds in New Zealand earlier this year, but he is not yet a fixture at the top of the order and will be disappointed not to have made runs here.
New man Trott took an early liking to Southee, hitting his fifth and sixth deliveries for four and adding a third boundary when he eased the first ball of the 10th over through cover.
Southee was otherwise impressive, though, while Trent Boult conceded just six runs in as many overs at the other end.
Neil Wagner's introduction in place of Boult immediately yielded a boundary, Trott's fourth of the day to long leg.
- Sports & Recreation
- Jonathan Trott
- Tim Southee
- Alastair Cook