After winning the toss and opting to bat first, Glamorgan made hay in the Manchester sun as they reached 315 for three off 97 overs at stumps.
Former Zimbabwe international Goodwin, 40, ended the day unbeaten on 138 while sharing in an unbroken 130-run stand with Jim Allenby (68no).
Earlier, Glamorgan opener Gareth Rees made 58 as in-form Lancashire, who have a one-point lead over Northamptonshire at the top of Division Two having played one game fewer, struggled to make any impression on a pitch that is good for batting on at the moment and expected to turn significantly later on.
Bat also largely dominated ball in the other Division Two match with Hampshire's Michael Carberry celebrating a century against former county Kent at Canterbury.
The 32 year-old left-hander, who spent three seasons at Kent before heading to Southampton at the end of 2005, hit a season's best 137 not out to help Hampshire post 263 for three at stumps.
He shared in a 146-run stand for the second wicket with Liam Dawson (75) and then put on an unbroken 71-run partnership with Sean Ervine (24 not out) as Hampshire enjoyed a productive day.
In the only Division One match, defending champions Warwickshire closed on 254 for six against mid-table rivals Nottinghamshire at Edgbaston.
Captain Varun Chopra and William Porterfield both fell for 10 early on, but Laurie Evans (85 not out), Ian Westwood (68) and Tim Ambrose (39) helped the hosts battle back in their first home match in two months due largely to last month's ICC Champions Trophy.
Andre Adams (three for 49) and Samit Patel (two for 40) were the most successful of Nottinghamshire's six-man bowling attack.
Warwickshire's own bowling stocks, meanwhile, have been depleted for the rest of the season with the news that England Lions seamer Chris Wright could be out for around six months with a stress fracture in his back.