On form Briggs had no problem adding the extras giving Ireland a 13-7 lead before USA out-half Kimber Rozier struck a penalty to close the gap.
It wasn't until the stroke of half time that Briggs added to Ireland's advantage touching down off the back of a ruck and duly converting giving the girls in green a 20-10 lead going into the break.
Barely a minute had elapsed in the second half when American lock Farmer muscled over from a couple of metres out. Rozier added the extras for 20-17.
There was little between the teams in a tight third quarter. Crucially though, centre Jenny Murphy made a terrific impact off the bench with two forceful runs - the second seeing her link well with Tania Rosser off another muscular maul from the pack.
The same attack led to USA replacement Shaina Turley picking up a yellow card close to her try-line and Briggs mopped up with a well-struck penalty right on the hour mark.
Briggs slid a drop goal attempt wide as Ireland tried to move clear by more than a converted try, entering the closing stages.
Their greater experience showed as they continued to control territory and a hard-won victory was theirs, albeit with Briggs missing a last-gasp penalty which would have denied the US their losing bonus point.
Next up for captain Fiona Coghlan and her team-mates is a fascinating first ever clash with New Zealand on Tuesday. The Black Ferns, who are the defending champions, overwhelmed Kazakhstan 79-5 earlier today.
This game will be televised live on TG4 and Sky or you can follow all Women's Rugby World Cup updates on #WRWC2014
To tweet your message of support for the Ireland Women you can use the hashtag #shouldertoshoulder
TIME LINE: 3 minutes - Ireland penalty: Niamh Briggs - 3-0; 6 mins - USA try: Lynelle Kugler - 3-5; conversion: Kimberly Rozier - 3-7; 11 mins - Ireland penalty: Niamh Briggs - 6-7; 29 mins - USA yellow card: Sarah Walsh; 30 mins - Ireland try: Ailis Egan - 11-7; conversion: Niamh Briggs - 13-7; 35 mins - Ireland yellow card: Claire Molloy; 36 mins - USA penalty: Kimberly Rozier - 13-10; 39 mins - Ireland try: Niamh Briggs - 18-10; conversion: Niamh Briggs - 20-10; Half-time - Ireland 20 USA 10; 42 mins - USA try: Carmen Farmer - 20-15; conversion: Kimberly Rozier - 20-17; 59 mins - USA yellow card: Shaina Turley; 60 mins - Ireland penalty: Niamh Briggs - 23-17; 80 mins - Ireland penalty: missed by Niamh Briggs - 23-17; Full-time - Ireland 23 USA 17
Referee: Sherry Trumbull (Canada)
The Ireland Women line up for the national anthem in France.
Ireland Women's Team v USA
15. Niamh Briggs (UL Bohemians/Munster)
14. Ashleigh Baxter (Belfast Harlequins/Ulster)
13. Lynne Cantwell (Richmond RFC/Exile)
12. Grace Davitt (Cooke/Ulster)
11. Alison Miller (Portlaoise/Connacht)
10. Nora Stapleton (Old Belvedere/Leinster)
9. Tania Rosser (Blackrock/Leinster)
1. Fiona Coghlan (UL Bohemians/Leinster)
2. Gillian Bourke (UL Bohemians/Munster)
3. Ailis Egan (Old Belvedere/Leinster)
4. Sophie Spence (Old Belvedere/Leinster)
5. Marie Louise Reilly (Old Belvedere/Leinster)
6. Siobhan Fleming (Tralee/Munster)
7. Claire Molloy (Bristol/Connacht)
8. Heather O'Brien (Highfield RFC/Munster)
16. Sharon Lynch (Old Belvedere/Leinster)
17. Fiona Hayes (UL Bohemians/Munster)
18. Laura Guest (Highfield/Munster)
19. Paula Fitzpatrick (St Mary's College/Leinster)
20. Larissa Muldoon (Bristol/Exile)
21. Jenny Murphy (Old Belvedere/Leinster)
22. Jackie Shiels (Richmond RFC/Exile)
2014 WOMEN'S RUGBY WORLD CUP:
POOL B FIXTURES -
Tuesday, August 5
New Zealand v IRELAND, Marcoussis pitch 1, 6pm local time/5pm Irish time
Saturday, August 9
IRELAND v Kazakhstan, Marcoussis pitch 2, 1pm local time/12pm Irish time