Assuming input file is tab-delimited. If not, reformat, or change the code below. Save code as sort_eval.py and run as python sort_eval.py file.txt

#!/usr/bin/env python
import sys
from collections import defaultdict

evalue = defaultdict(list)

with open(sys.argv[1], 'r') as f:
        next(f)
        for line in f:
                evalue[line.strip().split('\t')[0]].append(line.strip().split('\t')[1])

for i in sorted(evalue):
        print i, '\t', sorted(evalue[i])[0]

Output:

g1      0.0
g2      1e-13
g3      0.01

Something like this

show contents | remove header | sort based on first column followed by second | keep rows based on first occurrence of first column

code

cat test.test | grep -v ID | sort -k1,1 -k2,2n | awk '!a[$1]++'

result

g1 0.0
g2 1e-13
g3 0.01

P.S. You can directly pass input file to grep i.e. grep -v ID text.txt | ...