Opening batsman Trescothick's 113, his 11th century at this level, helped England to 301 for seven after stand-in captain Andrew Strauss won the toss.
Somerset left-hander Trescothick, who also shared a century stand with Ian Bell (80), won the man-of-the-match award after striking 14 boundaries in what was England's first One-dayer of the 2006 northern season.
Ireland, who had been 135 for six, creditably batted out their full 50 overs as they denied England the satisfaction of taking all 10 wickets.
Fast bowler Stephen Harmison, in his first England appearance since the second Test defeat in India, led the attack with three for 58 as he returned to international duty after shin problems.
But his new-ball partner Glen Chapple, one of three debutants, was forced off the field with an abdominal muscle injury.
South Africa-born Andre Botha's 52 was Ireland's only fifty of the match.
Earlier, opening batsman Ed Joyce, making his England debut against an Ireland side that included his brother Dominick, scored just 10.
The Dublin-born Middlesex batsman, attempting to pull seamer David Langford-Smith, presented Kevin O'Brien with a straightforward catch at mid-wicket.
Joyce's departure triggered a mini-collapse with England losing both Strauss (four) and Paul Collingwood (10) cheaply as they struggled to 92 for three after 14 overs.
But a determined display by Warwickshire batsman Bell and Trescothick's increasingly fluency got the visitors back on track and ensured Ireland were set a tough target.
Ireland have been granted full international status for a two-year period after qualifying for the 2007 World Cup in the West Indies.
For England, this match served as a warm-up for their five match limited overs series against Sri Lanka, starting at Lord's on Saturday.
But before then they face Sri Lanka in a one-off Twenty20 encounter on Thursday at Hampshire's Rose Bowl ground.
Fall of wickets: 1-36, 2-63, 3-92, 4-234, 5-258, 6-264, 7-285
Did not bat: S Harmison, S Mahmood
Fall of wickets: 1-10, 2-60, 3-118, 4-121, 5-127, 6-135
7-209, 8-210, 9-235
Result: England won by 38 runs
Man-of-the-match: Marcus Trescothick (ENG)
Umpires: Roger Dill (BER), Darrell Hair (AUS)
TV umpire: Austin Christopher (WIS)
Match referee: Clive Lloyd (WIS)