Kerber made the semi-finals at the Mallorca Open last week to kick off her grass court season and will be hopeful of claiming her first title of the year in Eastbourne, where she has twice reached the final.
Her opponent Sam Stosur was one of a host of players playing two matches in the one day after rain interrupted Monday's schedule.
The veteran Australian had seen off American Sofia Kenin in round one, but had no answer to Kerber's power as the German fired 15 winners in a 6-4, 6-4 victory.
"It's nice being back here, having another good match on grass before Wimbledon," said Kerber.
"That's why I'm here. I like to play here on grass, so I try to enjoy every match and every moment right now."
Bertens was also in commanding form as the number three seed saw off Yulia Putintseva 6-4, 6-1.
Defending champion Caroline Wozniacki won in straight sets too, beating Andrea Petkovic, 6-4, 6-4, to set up a rematch of last year's final against Aryna Sabalenka.
Konta is keen to make an impression on home soil after reaching the semi-finals of the French Open.
The world number 19 was pushed all the way by Greece's Maria Sakkari, but prevailed 6-4, 7-6 (7/4) to set up a round three clash with Ons Jabeur.
Sixth seed Halep began her grass court campaign in style with a 6-2, 6-0 thrashing of Su-Wei Hsieh and will be confident of further progress when she faces Slovakian qualifier Polona Hercog next.
Elena Svitolina was the top ranked player to exit on Tuesday as the Ukranian fifth seed bowed out 6-3, 7-6 (7/3) to Alize Cornet.
The Frenchwoman led by a set and a break before play was stopped on Monday, but Svitolina quickly broke back to level at 3-3 in the second and then saved a match point to break again and take it to a tie-break.
Cornet, however, bounced back to race through the tie-break 7-3.
Former French Open champion Jelena Ostapenko also rallied from losing the first set 6-1 to world number 9 Sloane Stephens to take the next two sets 6-0, 6-3.
Eastbourne ATP/WTA results on Tuesday (x denotes seeding):
Cameron Norrie (GBR) bt Jérémy Chardy (FRA) 6-3, 7-6 (7/4)
Pierre-Hugues Herbert (FRA) bt Denis Kudla (USA) 5-7, 7-6 (10/8), 6-4
Juan Ignacio Londero (ARG) bt Jay Clarke (GBR) 6-7 (5/7), 6-1, 6-3
Gilles Simon (FRA x6) bt Tennys Sandgren (USA) 7-5, 6-1
Nicolás Jarry (CHI) bt Pablo Cuevas (URU) 6-1, 7-6 (7/4)
Thomas Fabbiano (ITA) bt James Ward (GBR) 2-6, 6-3, 6-1
Ons Jabeur (TUN) bt Mandy Minella (LUX) 2-6, 6-2, 6-1
Johanna Konta (GBR x14) bt Maria Sakkari (GRE) 6-4, 7-6 (7/4)
Shuai Zhang (CHN) bt Daria Gavrilova (AUS) 6-3, 6-1
Alize Cornet (FRA) bt Elina Svitolina (UKR x5) 6-3, 7-6 (7/3)
Angelique Kerber (GER x4) bt Samantha Stosur (AUS) 6-4, 6-4
Rebecca Peterson (SWE) bt Lesya Tsurenko (UKR) 7-6 (8/6), 6-4
Polona Hercog (SLO) bt Pauline Parmentier (FRA) 2-6, 6-2, 7-6 (7/4)
Simona Halep (ROU x6) bt Su-Wei Hsieh (TPE) 6-2, 6-0
Aryna Sabalenka (BLR x8) bt Tamara Zidanšek (SLO) 6-2, 6-3
Caroline Wozniacki (DEN x11) bt Andrea Petkovic (GER) 6-4, 6-4
Anna-Lena Friedsam (GER) bt Anett Kontaveit (EST x16) 6-3, 6-4
Kiki Bertens (NED x3) bt Yulia Putintseva (KAZ) 6-4, 6-1
Jelena Ostapenko (LAT) bt Sloane Stephens (USA x7) 1-6, 6-0, 6-3
Ekaterina Alexandrova (RUS) bt Belinda Bencic (SUI x10) 6-7 (6/8), 6-2, 6-3
Elise Mertens (BEL) bt Markéta Vondroušová (CZE x13) 6-1, 5-7, 6-2
Samantha Stosur (AUS) bt Sofia Kenin (USA) 6-2, 6-3
Lesya Tsurenko (UKR) bt Zarina Diyas (KAZ) 6-2, 6-2
Polona Hercog (SLO) bt Barbora Záhlavová Strýcová (CZE) 7-6 (7/3), 0-1 abandon
Belinda Bencic (SUI x10) bt Veronika Kudermetova (RUS) 6-3, 6-4